Abstract
Identify the key drivers of brand equity for Galeries Lafayette based on a questionnaire mailed to 5000 customers and returned by 600 of themThis analysis was prepared by Francisco Arrieta and Jonathan Edwards.
# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"
# define table styling options
stable <- function(data, digits = 2) {
knitr::kable(data, digits=digits) |>
# kable_styling(c("striped", "condensed"))
kable_paper(full_width = F)
}# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs
# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr) #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test
# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion) #Histogram and Normal Curve
library(kableExtra) #makes nice tables
# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")
dim(survey)## [1] 553 45
# head(labels)#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]])
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels
#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
stable()| Variable | Category | Label_short |
|---|---|---|
| Im1 | What do GLB represent from your point of view | Large Assortment |
| Im2 | What do GLB represent from your point of view | Assortment Variety |
| Im3 | What do GLB represent from your point of view | Artistic Decoration of Sales Area |
| Im4 | What do GLB represent from your point of view | Creative Decoration of Sales Area |
| Im5 | What do GLB represent from your point of view | Appealing Arrangement of Shop Windows |
| Im6 | What do GLB represent from your point of view | France |
| Im7 | What do GLB represent from your point of view | French Savoir-vivre |
| Im8 | What do GLB represent from your point of view | Expertise in French Traditional Cuisine |
| Im9 | What do GLB represent from your point of view | French Fashion |
| Im10 | What do GLB represent from your point of view | Gourmet Food |
| Im11 | What do GLB represent from your point of view | High-quality Cosmetics |
| Im12 | What do GLB represent from your point of view | Luxury brands |
| Im13 | What do GLB represent from your point of view | Up tp date Designer Brands |
| Im14 | What do GLB represent from your point of view | Gourmet specialities |
| Im15 | What do GLB represent from your point of view | Professional Selection of Brands |
| Im16 | What do GLB represent from your point of view | Professional Appearance Towards Customers |
| Im17 | What do GLB represent from your point of view | Are Trendy |
| Im18 | What do GLB represent from your point of view | Are Hip |
| Im19 | What do GLB represent from your point of view | Professional Organization |
| Im20 | What do GLB represent from your point of view | Relaxing Shopping |
| Im21 | What do GLB represent from your point of view | A Great Place to Stroll |
| Im22 | What do GLB represent from your point of view | Intimate Shop Atmosphere |
| C_CR1 | CO-CREATION | I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin. |
| C_CR2 | CO-CREATION | I would be available to take part in another survey at Galeries Lafayette Berlin. |
| C_CR3 | CO-CREATION | I would like to become a member of a customer group whose opinion is obtained for new products and major changes. |
| C_CR4 | CO-CREATION | I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked. |
| C_REP1 | REPURCHASE | I will continue to be a loyal customer of Galeries Lafayette Berlin. |
| C_REP2 | REPURCHASE | I intend to shop at Galeries Lafayette Berlin in the future. |
| C_REP3 | REPURCAHSE | I will surely visit Galeries Lafayette Berlin in the future. |
| COM_A1 | AFFECTIVE COMMITMENT | How strongly are you attached to Galeries Lafayette Berlin? |
| COM_A2 | AFFECTIVE COMMITMENT | How strongly are you emotionally connected to Galeries Lafayette Berlin? |
| COM_A3 | AFFECTIVE COMMITMENT | As a customer I feel (close) attached to GL |
| COM_A4 | AFFECTIVE COMMITMENT | feel a strong emotional bond toward GLB |
| SAT_1 | SATISFACTION | I am very satisfied with Galeries Lafayette Berlin. |
| SAT_2 | SATISFACTION | Overall, I am very satisfied with Galeries Lafayette Berlin. |
| SAT_3 | SATISFACTION | How satisfied are you with Galeries Lafayette Berlin? |
| SAT_P1 | SATISFACTION EMPLOYEES | The employees are capable and professional. |
| SAT_P2 | SATISFACTION EMPLOYEES | The employees know best about their products. |
| SAT_P3 | SATISFACTION EMPLOYEES | The employees are well-informed. |
| SAT_P4 | SATISFACTION EMPLOYEES | The employees are always helpful. |
| SAT_P5 | SATISFACTION EMPLOYEES | The employees are willing to respond to my questions in detail. |
| SAT_P6 | SATISFACTION EMPLOYEES | The employees are friendly. |
| TRU_1 | TRUST | I have the feeling that I can completely rely on GL. |
| TRU_2 | TRUST | GLB will always be honest and trustful with me. |
| TRU_3 | TRUST | GL will treat me always fair as a customer |
# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
#
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
#
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))# delete variables unused in analysis (see case study instructions):
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))
# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c()
# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)
dim(survey)## [1] 553 35
dim(survey_excl_img)## [1] 553 35
dim(data_img_EFA)## [1] 385 22
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Variables to look out for going forward:
Images 9 and 11 are alone
Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA)
##
## X2 = 6451.238
## df = 231
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA)
##
## Measures of Sampling Adequacy (MSA):
## Im2 Im6 Im1 Im20 Im14 Im10 Im7 Im4
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604
## Im18 Im3 Im17 Im13 Im12 Im22 Im16 Im11
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882
## Im21 Im8 Im9 Im19 Im5 Im15
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563
##
## KMO-Criterion: 0.8770975
The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
# Sort table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
# Display table
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im2 | 0.82 |
| Im6 | 0.82 |
| Im1 | 0.82 |
| Im20 | 0.83 |
| Im14 | 0.83 |
| Im10 | 0.83 |
| Im7 | 0.84 |
| Im4 | 0.85 |
| Im18 | 0.86 |
| Im3 | 0.86 |
| Im17 | 0.86 |
| Im13 | 0.87 |
| Im12 | 0.88 |
| Im22 | 0.88 |
| Im16 | 0.91 |
| Im11 | 0.91 |
| Im21 | 0.91 |
| Im8 | 0.93 |
| Im9 | 0.94 |
| Im19 | 0.94 |
| Im5 | 0.95 |
| Im15 | 0.96 |
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable() | Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 8.98 | 40.81 | 0.41 |
| 2 | 2.47 | 11.21 | 0.52 |
| 3 | 1.56 | 7.10 | 0.59 |
| 4 | 1.46 | 6.62 | 0.66 |
| 5 | 1.25 | 5.67 | 0.71 |
| 6 | 1.15 | 5.22 | 0.77 |
| 7 | 0.81 | 3.68 | 0.80 |
| 8 | 0.71 | 3.23 | 0.84 |
| 9 | 0.57 | 2.58 | 0.86 |
| 10 | 0.46 | 2.08 | 0.88 |
| 11 | 0.36 | 1.64 | 0.90 |
| 12 | 0.33 | 1.51 | 0.91 |
| 13 | 0.29 | 1.34 | 0.93 |
| 14 | 0.28 | 1.29 | 0.94 |
| 15 | 0.25 | 1.13 | 0.95 |
| 16 | 0.23 | 1.04 | 0.96 |
| 17 | 0.20 | 0.92 | 0.97 |
| 18 | 0.19 | 0.85 | 0.98 |
| 19 | 0.16 | 0.72 | 0.99 |
| 20 | 0.12 | 0.53 | 0.99 |
| 21 | 0.10 | 0.46 | 1.00 |
| 22 | 0.08 | 0.37 | 1.00 |
With 6 factors we would explain 76.6310791% of total variance.
With 7 factors we would explain 80.3133487% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 8.377985
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.405600881872799”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.463399199002637”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455673655610471”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455554069181416”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR4 | MR1 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.31 | 0.18 | ||||
| Im2 | 0.83 | 1.23 | 0.24 | ||||
| Im3 | 0.83 | 1.55 | 0.14 | ||||
| Im4 | 0.87 | 1.46 | 0.08 | ||||
| Im5 | 0.64 | 1.78 | 0.45 | ||||
| Im6 | 0.67 | 1.22 | 0.50 | ||||
| Im7 | 0.79 | 1.20 | 0.31 | ||||
| Im8 | 0.84 | 1.16 | 0.24 | ||||
| Im9 | 0.43 | 0.39 | 2.76 | 0.59 | |||
| Im10 | 0.75 | 1.37 | 0.34 | ||||
| Im11 | 0.57 | 1.56 | 0.59 | ||||
| Im12 | 0.79 | 1.27 | 0.29 | ||||
| Im13 | 0.77 | 1.43 | 0.28 | ||||
| Im14 | 0.75 | 1.37 | 0.34 | ||||
| Im15 | 0.60 | 0.33 | 2.66 | 0.37 | |||
| Im16 | 0.48 | 0.37 | 2.77 | 0.54 | |||
| Im17 | 0.38 | 0.48 | 3.44 | 0.46 | |||
| Im18 | 0.31 | 0.43 | 3.42 | 0.57 | |||
| Im19 | 0.47 | 0.40 | 3.37 | 0.47 | |||
| Im20 | 0.78 | 1.27 | 0.31 | ||||
| Im21 | 0.74 | 1.41 | 0.35 | ||||
| Im22 | 0.81 | 1.51 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.30 | 0.16 | |||||
| Im2 | 0.83 | 1.24 | 0.24 | |||||
| Im3 | 0.83 | 1.51 | 0.15 | |||||
| Im4 | 0.88 | 1.42 | 0.08 | |||||
| Im5 | 0.64 | 1.74 | 0.45 | |||||
| Im6 | 0.61 | 0.56 | 2.12 | 0.29 | ||||
| Im7 | 0.72 | 0.48 | 1.88 | 0.22 | ||||
| Im8 | 0.81 | 1.25 | 0.26 | |||||
| Im9 | 0.35 | 0.32 | 0.43 | 3.51 | 0.54 | |||
| Im10 | 0.80 | 1.42 | 0.22 | |||||
| Im11 | 0.59 | 1.62 | 0.55 | |||||
| Im12 | 0.79 | 1.34 | 0.27 | |||||
| Im13 | 0.73 | 1.66 | 0.30 | |||||
| Im14 | 0.80 | 1.42 | 0.24 | |||||
| Im15 | 0.60 | 2.76 | 0.37 | |||||
| Im16 | 0.48 | 0.37 | 2.78 | 0.53 | ||||
| Im17 | 0.35 | 0.31 | 0.39 | 0.54 | 3.66 | 0.30 | ||
| Im18 | 0.35 | 0.50 | 3.48 | 0.43 | ||||
| Im19 | 0.46 | 0.40 | 3.45 | 0.48 | ||||
| Im20 | 0.84 | 1.22 | 0.21 | |||||
| Im21 | 0.73 | 1.43 | 0.35 | |||||
| Im22 | 0.79 | 1.60 | 0.21 |
| Variable | MR5 | MR1 | MR3 | MR2 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.33 | 0.14 | ||||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||||
| Im3 | 0.83 | 1.56 | 0.14 | ||||||
| Im4 | 0.90 | 1.40 | 0.03 | ||||||
| Im5 | 0.63 | 1.85 | 0.46 | ||||||
| Im6 | 0.83 | 1.25 | 0.24 | ||||||
| Im7 | 0.32 | 0.84 | 1.44 | 0.15 | |||||
| Im8 | 0.63 | 0.51 | 2.31 | 0.28 | |||||
| Im9 | 0.33 | 0.45 | 3.45 | 0.54 | |||||
| Im10 | 0.87 | 1.35 | 0.11 | ||||||
| Im11 | 0.58 | 1.72 | 0.56 | ||||||
| Im12 | 0.85 | 1.30 | 0.17 | ||||||
| Im13 | 0.72 | 1.81 | 0.30 | ||||||
| Im14 | 0.81 | 1.50 | 0.19 | ||||||
| Im15 | 0.59 | 2.97 | 0.37 | ||||||
| Im16 | 0.46 | 0.34 | 3.44 | 0.53 | |||||
| Im17 | 0.84 | 1.76 | 0.05 | ||||||
| Im18 | 0.72 | 1.85 | 0.29 | ||||||
| Im19 | 0.43 | 0.37 | 4.25 | 0.47 | |||||
| Im20 | 0.85 | 1.21 | 0.21 | ||||||
| Im21 | 0.73 | 1.44 | 0.35 | ||||||
| Im22 | 0.78 | 1.62 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR7 | MR2 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.88 | 1.45 | 0.06 | |||||||
| Im2 | 0.82 | 1.45 | 0.19 | |||||||
| Im3 | 0.81 | 1.66 | 0.14 | |||||||
| Im4 | 0.89 | 1.47 | 0.03 | |||||||
| Im5 | 0.65 | 1.84 | 0.42 | |||||||
| Im6 | 0.83 | 1.23 | 0.24 | |||||||
| Im7 | 0.84 | 0.30 | 1.40 | 0.15 | ||||||
| Im8 | 0.54 | 0.59 | 2.56 | 0.28 | ||||||
| Im9 | 0.33 | 0.46 | 3.34 | 0.54 | ||||||
| Im10 | 0.87 | 1.41 | 0.10 | |||||||
| Im11 | 0.58 | 1.72 | 0.55 | |||||||
| Im12 | 0.86 | 1.28 | 0.16 | |||||||
| Im13 | 0.72 | 1.78 | 0.30 | |||||||
| Im14 | 0.83 | 1.49 | 0.15 | |||||||
| Im15 | 0.47 | 0.39 | 4.81 | 0.35 | ||||||
| Im16 | 0.77 | 1.78 | 0.20 | |||||||
| Im17 | 0.82 | 1.82 | 0.07 | |||||||
| Im18 | 0.74 | 1.76 | 0.26 | |||||||
| Im19 | 0.30 | 0.54 | 3.68 | 0.38 | ||||||
| Im20 | 0.86 | 1.20 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.35 | |||||||
| Im22 | 0.78 | 1.63 | 0.22 |
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.
Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.
Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.
We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.272947652560888”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.339338697735652”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.279736181915467”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.302814913694533”
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.06 | 0.18 | ||||
| Im2 | 1.07 | 1.07 | 0.24 | ||||
| Im3 | 1.00 | 1.03 | 0.14 | ||||
| Im4 | 1.07 | 1.03 | 0.08 | ||||
| Im5 | 0.75 | 1.03 | 0.45 | ||||
| Im6 | 0.73 | 1.11 | 0.50 | ||||
| Im7 | 0.87 | 1.14 | 0.31 | ||||
| Im8 | 0.91 | 1.01 | 0.24 | ||||
| Im9 | 0.36 | 0.37 | 2.10 | 0.59 | |||
| Im10 | 0.77 | 1.17 | 0.34 | ||||
| Im11 | 0.69 | 1.08 | 0.59 | ||||
| Im12 | 1.00 | 1.05 | 0.29 | ||||
| Im13 | 0.94 | 1.03 | 0.28 | ||||
| Im14 | 0.77 | 1.12 | 0.34 | ||||
| Im15 | 0.62 | 1.14 | 0.37 | ||||
| Im16 | 0.47 | 1.79 | 0.54 | ||||
| Im17 | 0.42 | 2.05 | 0.46 | ||||
| Im18 | 0.39 | 1.93 | 0.57 | ||||
| Im19 | 0.41 | 2.02 | 0.47 | ||||
| Im20 | 0.86 | 1.04 | 0.31 | ||||
| Im21 | 0.79 | 1.09 | 0.35 | ||||
| Im22 | 0.85 | 1.02 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.05 | 1.06 | 0.16 | |||||
| Im2 | 1.03 | 1.07 | 0.24 | |||||
| Im3 | 0.99 | 1.03 | 0.15 | |||||
| Im4 | 1.06 | 1.05 | 0.08 | |||||
| Im5 | 0.74 | 1.03 | 0.45 | |||||
| Im6 | 0.52 | 0.68 | 2.22 | 0.29 | ||||
| Im7 | 0.65 | 0.56 | 2.24 | 0.22 | ||||
| Im8 | 0.80 | 1.05 | 0.26 | |||||
| Im9 | 0.48 | 1.95 | 0.54 | |||||
| Im10 | 0.81 | 1.23 | 0.22 | |||||
| Im11 | 0.67 | 1.15 | 0.55 | |||||
| Im12 | 0.91 | 1.03 | 0.27 | |||||
| Im13 | 0.79 | 1.09 | 0.30 | |||||
| Im14 | 0.80 | 1.18 | 0.24 | |||||
| Im15 | 0.60 | 1.18 | 0.37 | |||||
| Im16 | 0.46 | 1.81 | 0.53 | |||||
| Im17 | 0.57 | 1.97 | 0.30 | |||||
| Im18 | 0.54 | 1.91 | 0.43 | |||||
| Im19 | 0.39 | 2.15 | 0.48 | |||||
| Im20 | 0.92 | 1.07 | 0.21 | |||||
| Im21 | 0.76 | 1.07 | 0.35 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR5 | MR1 | MR2 | MR3 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.08 | 1.06 | 0.14 | ||||||
| Im2 | 1.05 | 1.06 | 0.22 | ||||||
| Im3 | 1.00 | 1.02 | 0.14 | ||||||
| Im4 | 1.13 | 1.04 | 0.03 | ||||||
| Im5 | 0.72 | 1.02 | 0.46 | ||||||
| Im6 | 0.92 | 1.06 | 0.24 | ||||||
| Im7 | 0.89 | 1.06 | 0.15 | ||||||
| Im8 | 0.62 | 0.38 | 1.74 | 0.28 | |||||
| Im9 | 0.42 | 2.10 | 0.54 | ||||||
| Im10 | 1.04 | 1.03 | 0.11 | ||||||
| Im11 | 0.65 | 1.14 | 0.56 | ||||||
| Im12 | 1.01 | 1.04 | 0.17 | ||||||
| Im13 | 0.78 | 1.08 | 0.30 | ||||||
| Im14 | 0.94 | 1.01 | 0.19 | ||||||
| Im15 | 0.60 | 1.17 | 0.37 | ||||||
| Im16 | 0.40 | 2.69 | 0.53 | ||||||
| Im17 | 1.09 | 1.02 | 0.05 | ||||||
| Im18 | 0.92 | 1.02 | 0.29 | ||||||
| Im19 | 0.33 | 3.23 | 0.47 | ||||||
| Im20 | 0.94 | 1.05 | 0.21 | ||||||
| Im21 | 0.78 | 1.06 | 0.35 | ||||||
| Im22 | 0.81 | 1.05 | 0.21 |
| Variable | MR1 | MR3 | MR7 | MR2 | MR4 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.01 | 0.06 | |||||||
| Im2 | 0.95 | 1.02 | 0.19 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.03 | 1.03 | 0.03 | |||||||
| Im5 | 0.72 | 1.11 | 0.42 | |||||||
| Im6 | 0.98 | 1.06 | 0.24 | |||||||
| Im7 | 0.95 | 1.05 | 0.15 | |||||||
| Im8 | 0.43 | 0.49 | 2.39 | 0.28 | ||||||
| Im9 | 0.45 | 1.92 | 0.54 | |||||||
| Im10 | 0.97 | 1.01 | 0.10 | |||||||
| Im11 | 0.66 | 1.15 | 0.55 | |||||||
| Im12 | 1.04 | 1.05 | 0.16 | |||||||
| Im13 | 0.79 | 1.06 | 0.30 | |||||||
| Im14 | 0.92 | 1.02 | 0.15 | |||||||
| Im15 | 0.35 | 0.36 | 2.73 | 0.35 | ||||||
| Im16 | 1.02 | 1.03 | 0.20 | |||||||
| Im17 | 0.98 | 1.01 | 0.07 | |||||||
| Im18 | 0.90 | 1.01 | 0.26 | |||||||
| Im19 | 0.63 | 1.11 | 0.38 | |||||||
| Im20 | 0.98 | 1.09 | 0.19 | |||||||
| Im21 | 0.79 | 1.06 | 0.35 | |||||||
| Im22 | 0.82 | 1.06 | 0.22 |
7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18
# # perform multiple variable selections
#
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
# c("Im3","Im4","Im9", "Im15","Im11"))
#
# survey_excl_img2 = list()
# data_img_EFA2 = list()
#
# for (i in 1:length(exclude)){
# survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
# data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
# # print(survey_excl_img2[[i]])
# }
#
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"
exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"
# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]The excluded variables correspond to the following:
excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")]
excludedvars |>
stable()| Variable | Label_short |
|---|---|
| Im8 | Expertise in French Traditional Cuisine |
| Im9 | French Fashion |
| Im15 | Professional Selection of Brands |
# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)
dim(survey)## [1] 553 35
dim(survey_excl_img2)## [1] 553 32
dim(data_img_EFA2)## [1] 394 19
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA2)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA2)
##
## X2 = 5521.451
## df = 171
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA2)
##
## Measures of Sampling Adequacy (MSA):
## Im6 Im10 Im7 Im14 Im2 Im1 Im20 Im18
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628
## Im4 Im17 Im12 Im3 Im13 Im22 Im11 Im16
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282
## Im21 Im19 Im5
## 0.9102753 0.9199391 0.9515411
##
## KMO-Criterion: 0.8416876
The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
#Display table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im6 | 0.75 |
| Im10 | 0.76 |
| Im7 | 0.77 |
| Im14 | 0.78 |
| Im2 | 0.80 |
| Im1 | 0.80 |
| Im20 | 0.81 |
| Im18 | 0.83 |
| Im4 | 0.84 |
| Im17 | 0.84 |
| Im12 | 0.85 |
| Im3 | 0.85 |
| Im13 | 0.86 |
| Im22 | 0.87 |
| Im11 | 0.90 |
| Im16 | 0.90 |
| Im21 | 0.91 |
| Im19 | 0.92 |
| Im5 | 0.95 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable()| Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 7.71 | 40.57 | 0.41 |
| 2 | 2.01 | 10.58 | 0.51 |
| 3 | 1.54 | 8.10 | 0.59 |
| 4 | 1.44 | 7.58 | 0.67 |
| 5 | 1.20 | 6.30 | 0.73 |
| 6 | 1.06 | 5.56 | 0.79 |
| 7 | 0.80 | 4.21 | 0.83 |
| 8 | 0.68 | 3.60 | 0.87 |
| 9 | 0.50 | 2.65 | 0.89 |
| 10 | 0.34 | 1.81 | 0.91 |
| 11 | 0.32 | 1.67 | 0.93 |
| 12 | 0.30 | 1.58 | 0.94 |
| 13 | 0.23 | 1.20 | 0.95 |
| 14 | 0.21 | 1.10 | 0.97 |
| 15 | 0.19 | 1.02 | 0.98 |
| 16 | 0.16 | 0.84 | 0.98 |
| 17 | 0.12 | 0.62 | 0.99 |
| 18 | 0.11 | 0.57 | 1.00 |
| 19 | 0.08 | 0.43 | 1.00 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
With 6 factors we would explain 78.6947762% of total variance.
With 7 factors we would explain 82.9058259% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 7.109148
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.496673139129337”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.638799740882147”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.931925021212407”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =0.990898460352201”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR4 | MR5 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.35 | 0.16 | ||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||
| Im3 | 0.84 | 1.44 | 0.14 | ||||
| Im4 | 0.89 | 1.36 | 0.08 | ||||
| Im5 | 0.65 | 1.66 | 0.45 | ||||
| Im6 | 0.67 | 1.23 | 0.50 | ||||
| Im7 | 0.78 | 1.20 | 0.33 | ||||
| Im10 | 0.74 | 1.42 | 0.34 | ||||
| Im11 | 0.58 | 1.49 | 0.59 | ||||
| Im12 | 0.82 | 1.22 | 0.25 | ||||
| Im13 | 0.77 | 1.44 | 0.28 | ||||
| Im14 | 0.77 | 1.39 | 0.30 | ||||
| Im16 | 0.40 | 0.41 | 3.03 | 0.58 | |||
| Im17 | 0.30 | 0.43 | 0.39 | 3.76 | 0.48 | ||
| Im18 | 0.39 | 0.32 | 3.81 | 0.58 | |||
| Im19 | 0.42 | 0.43 | 3.53 | 0.49 | |||
| Im20 | 0.80 | 1.23 | 0.28 | ||||
| Im21 | 0.74 | 1.39 | 0.36 | ||||
| Im22 | 0.81 | 1.49 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR4 | MR5 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.40 | 0.11 | |||||
| Im2 | 0.83 | 1.33 | 0.20 | |||||
| Im3 | 0.85 | 1.43 | 0.14 | |||||
| Im4 | 0.89 | 1.35 | 0.08 | |||||
| Im5 | 0.65 | 1.63 | 0.45 | |||||
| Im6 | 0.73 | 1.40 | 0.36 | |||||
| Im7 | 0.81 | 1.24 | 0.27 | |||||
| Im10 | 0.70 | 0.32 | 1.95 | 0.29 | ||||
| Im11 | 0.61 | 1.46 | 0.55 | |||||
| Im12 | 0.80 | 1.31 | 0.26 | |||||
| Im13 | 0.71 | 1.80 | 0.31 | |||||
| Im14 | 0.73 | 0.32 | 1.85 | 0.26 | ||||
| Im16 | 0.41 | 0.39 | 3.16 | 0.58 | ||||
| Im17 | 0.74 | 2.15 | 0.17 | |||||
| Im18 | 0.66 | 2.10 | 0.35 | |||||
| Im19 | 0.43 | 0.39 | 3.93 | 0.49 | ||||
| Im20 | 0.84 | 1.21 | 0.22 | |||||
| Im21 | 0.73 | 1.43 | 0.36 | |||||
| Im22 | 0.79 | 1.54 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.87 | 1.40 | 0.09 | ||||||
| Im2 | 0.83 | 1.35 | 0.19 | ||||||
| Im3 | 0.84 | 1.46 | 0.14 | ||||||
| Im4 | 0.92 | 1.33 | 0.03 | ||||||
| Im5 | 0.64 | 1.73 | 0.45 | ||||||
| Im6 | 0.93 | 1.17 | 0.07 | ||||||
| Im7 | 0.33 | 0.75 | 1.62 | 0.28 | |||||
| Im10 | 0.92 | 1.32 | 0.03 | ||||||
| Im11 | 0.57 | 1.70 | 0.57 | ||||||
| Im12 | 0.88 | 1.23 | 0.13 | ||||||
| Im13 | 0.72 | 1.76 | 0.31 | ||||||
| Im14 | 0.77 | 0.30 | 1.67 | 0.22 | |||||
| Im16 | 0.38 | 0.37 | 3.99 | 0.57 | |||||
| Im17 | 0.88 | 1.60 | 0.00 | ||||||
| Im18 | 0.70 | 1.84 | 0.33 | ||||||
| Im19 | 0.40 | 0.37 | 4.52 | 0.49 | |||||
| Im20 | 0.85 | 1.19 | 0.21 | ||||||
| Im21 | 0.73 | 1.43 | 0.36 | ||||||
| Im22 | 0.79 | 1.55 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR7 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.91 | 1.44 | 0.00 | |||||||
| Im2 | 0.78 | 1.56 | 0.24 | |||||||
| Im3 | 0.82 | 1.63 | 0.14 | |||||||
| Im4 | 0.89 | 1.46 | 0.03 | |||||||
| Im5 | 0.66 | 1.78 | 0.42 | |||||||
| Im6 | 0.96 | 1.15 | 0.01 | |||||||
| Im7 | 0.34 | 0.72 | 1.69 | 0.31 | ||||||
| Im10 | 0.93 | 1.32 | 0.00 | |||||||
| Im11 | 0.57 | 1.71 | 0.57 | |||||||
| Im12 | 0.89 | 1.22 | 0.13 | |||||||
| Im13 | 0.72 | 1.76 | 0.31 | |||||||
| Im14 | 0.77 | 1.68 | 0.22 | |||||||
| Im16 | 0.68 | 2.03 | 0.33 | |||||||
| Im17 | 0.88 | 1.65 | 0.00 | |||||||
| Im18 | 0.70 | 1.84 | 0.32 | |||||||
| Im19 | 0.64 | 2.71 | 0.30 | |||||||
| Im20 | 0.86 | 1.19 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.36 | |||||||
| Im22 | 0.79 | 1.56 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.547199381232095”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.833006250441541”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.971113915290573”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =1.14058133882705”
# loadings for all selected number of factors
test = list()
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR5 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.06 | 1.05 | 0.16 | ||||
| Im2 | 1.06 | 1.07 | 0.22 | ||||
| Im3 | 1.05 | 1.04 | 0.14 | ||||
| Im4 | 1.11 | 1.05 | 0.08 | ||||
| Im5 | 0.77 | 1.03 | 0.45 | ||||
| Im6 | 0.72 | 1.12 | 0.50 | ||||
| Im7 | 0.85 | 1.15 | 0.33 | ||||
| Im10 | 0.75 | 1.21 | 0.34 | ||||
| Im11 | 0.68 | 1.09 | 0.59 | ||||
| Im12 | 1.00 | 1.04 | 0.25 | ||||
| Im13 | 0.89 | 1.02 | 0.28 | ||||
| Im14 | 0.78 | 1.14 | 0.30 | ||||
| Im16 | 0.33 | 0.36 | 2.14 | 0.58 | |||
| Im17 | 0.34 | 2.56 | 0.48 | ||||
| Im18 | 0.31 | 2.71 | 0.58 | ||||
| Im19 | 0.32 | 0.36 | 2.28 | 0.49 | |||
| Im20 | 0.88 | 1.07 | 0.28 | ||||
| Im21 | 0.78 | 1.06 | 0.36 | ||||
| Im22 | 0.84 | 1.02 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR5 | MR4 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.05 | 0.11 | |||||
| Im2 | 1.00 | 1.04 | 0.20 | |||||
| Im3 | 1.02 | 1.05 | 0.14 | |||||
| Im4 | 1.08 | 1.05 | 0.08 | |||||
| Im5 | 0.76 | 1.03 | 0.45 | |||||
| Im6 | 0.84 | 1.39 | 0.36 | |||||
| Im7 | 0.91 | 1.18 | 0.27 | |||||
| Im10 | 0.68 | 1.69 | 0.29 | |||||
| Im11 | 0.67 | 1.05 | 0.55 | |||||
| Im12 | 0.91 | 1.06 | 0.26 | |||||
| Im13 | 0.77 | 1.22 | 0.31 | |||||
| Im14 | 0.71 | 1.55 | 0.26 | |||||
| Im16 | 0.33 | 0.33 | 2.12 | 0.58 | ||||
| Im17 | 0.77 | 1.14 | 0.17 | |||||
| Im18 | 0.69 | 1.14 | 0.35 | |||||
| Im19 | 0.33 | 2.58 | 0.49 | |||||
| Im20 | 0.91 | 1.08 | 0.22 | |||||
| Im21 | 0.75 | 1.06 | 0.36 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR1 | MR3 | MR5 | MR4 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.05 | 0.09 | ||||||
| Im2 | 1.02 | 1.03 | 0.19 | ||||||
| Im3 | 1.01 | 1.02 | 0.14 | ||||||
| Im4 | 1.14 | 1.05 | 0.03 | ||||||
| Im5 | 0.73 | 1.02 | 0.45 | ||||||
| Im6 | 0.98 | 1.04 | 0.07 | ||||||
| Im7 | 0.73 | 1.16 | 0.28 | ||||||
| Im10 | 1.10 | 1.03 | 0.03 | ||||||
| Im11 | 0.60 | 1.16 | 0.57 | ||||||
| Im12 | 1.00 | 1.03 | 0.13 | ||||||
| Im13 | 0.75 | 1.11 | 0.31 | ||||||
| Im14 | 0.87 | 1.04 | 0.22 | ||||||
| Im16 | 3.60 | 0.57 | |||||||
| Im17 | 1.12 | 1.02 | 0.00 | ||||||
| Im18 | 0.86 | 1.03 | 0.33 | ||||||
| Im19 | 3.47 | 0.49 | |||||||
| Im20 | 0.94 | 1.04 | 0.21 | ||||||
| Im21 | 0.77 | 1.05 | 0.36 | ||||||
| Im22 | 0.82 | 1.03 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR2 | MR5 | MR6 | MR7 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.03 | 1.01 | 0.00 | |||||||
| Im2 | 0.86 | 1.01 | 0.24 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.02 | 1.03 | 0.03 | |||||||
| Im5 | 0.73 | 1.09 | 0.42 | |||||||
| Im6 | 1.06 | 1.03 | 0.01 | |||||||
| Im7 | 0.72 | 1.14 | 0.31 | |||||||
| Im10 | 1.05 | 1.02 | 0.00 | |||||||
| Im11 | 0.60 | 1.15 | 0.57 | |||||||
| Im12 | 1.02 | 1.04 | 0.13 | |||||||
| Im13 | 0.75 | 1.09 | 0.31 | |||||||
| Im14 | 0.82 | 1.03 | 0.22 | |||||||
| Im16 | 0.80 | 1.02 | 0.33 | |||||||
| Im17 | 1.03 | 1.01 | 0.00 | |||||||
| Im18 | 0.81 | 1.00 | 0.32 | |||||||
| Im19 | 0.72 | 1.04 | 0.30 | |||||||
| Im20 | 0.97 | 1.09 | 0.19 | |||||||
| Im21 | 0.77 | 1.05 | 0.36 | |||||||
| Im22 | 0.82 | 1.04 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
We test whether the constructs found in the exploratory phase adequately describe what is going on.
# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")
summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 110 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
##
## Number of observations 553
## Number of missing patterns 87
##
## Model Test User Model:
##
## Test statistic 1442.584
## Degrees of freedom 194
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8838.959
## Degrees of freedom 231
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.855
## Tucker-Lewis Index (TLI) 0.827
##
## Robust Comparative Fit Index (CFI) 0.854
## Robust Tucker-Lewis Index (TLI) 0.827
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -15479.697
## Loglikelihood unrestricted model (H1) -14758.405
##
## Akaike (AIC) 31121.394
## Bayesian (BIC) 31470.938
## Sample-size adjusted Bayesian (SABIC) 31213.808
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.108
## 90 Percent confidence interval - lower 0.103
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Robust RMSEA 0.110
## 90 Percent confidence interval - lower 0.105
## 90 Percent confidence interval - upper 0.116
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.092
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.936
## Im4 1.057 0.025 42.551 0.000 1.307 0.970
## Im5 0.820 0.034 23.857 0.000 1.013 0.761
## FRENCH =~
## Im6 1.000 0.642 0.535
## Im7 1.219 0.106 11.525 0.000 0.783 0.644
## Im8 1.244 0.099 12.567 0.000 0.799 0.755
## Im10 1.251 0.095 13.133 0.000 0.803 0.914
## Im14 1.244 0.095 13.142 0.000 0.799 0.929
## ATMOS =~
## Im20 1.000 1.268 0.848
## Im21 0.848 0.041 20.879 0.000 1.075 0.785
## Im22 1.053 0.046 22.697 0.000 1.335 0.873
## QUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.050 0.000 0.991 0.872
## Im13 1.465 0.105 13.982 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.232 0.926
## Im2 0.942 0.027 34.780 0.000 1.160 0.902
## Im15 0.720 0.036 20.097 0.000 0.887 0.740
## Im16 0.567 0.041 13.849 0.000 0.699 0.579
## Im19 0.540 0.038 14.310 0.000 0.666 0.592
## BRAND =~
## Im17 1.000 1.184 0.952
## Im18 1.025 0.038 27.280 0.000 1.214 0.868
## Im9 0.540 0.047 11.386 0.000 0.640 0.474
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FRENCH 0.344 0.046 7.416 0.000 0.434 0.434
## ATMOS 0.730 0.082 8.901 0.000 0.466 0.466
## QUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.782 0.079 9.940 0.000 0.514 0.514
## BRAND 0.778 0.076 10.268 0.000 0.531 0.531
## FRENCH ~~
## ATMOS 0.265 0.045 5.888 0.000 0.326 0.326
## QUAL 0.206 0.030 6.812 0.000 0.456 0.456
## CHOICE 0.299 0.044 6.737 0.000 0.378 0.378
## BRAND 0.277 0.042 6.547 0.000 0.364 0.364
## ATMOS ~~
## QUAL 0.373 0.053 7.021 0.000 0.419 0.419
## CHOICE 0.767 0.083 9.216 0.000 0.491 0.491
## BRAND 0.792 0.081 9.797 0.000 0.528 0.528
## QUAL ~~
## CHOICE 0.460 0.054 8.585 0.000 0.531 0.531
## BRAND 0.483 0.053 9.113 0.000 0.581 0.581
## CHOICE ~~
## BRAND 0.864 0.078 11.040 0.000 0.592 0.592
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.994 0.056 88.528 0.000 4.994 3.785
## .Im4 4.997 0.057 86.919 0.000 4.997 3.709
## .Im5 5.034 0.057 87.796 0.000 5.034 3.785
## .Im6 5.824 0.051 113.338 0.000 5.824 4.849
## .Im7 5.751 0.053 109.497 0.000 5.751 4.727
## .Im8 6.000 0.045 133.008 0.000 6.000 5.671
## .Im10 6.100 0.037 163.041 0.000 6.100 6.945
## .Im14 6.139 0.037 166.909 0.000 6.139 7.138
## .Im20 4.672 0.064 73.182 0.000 4.672 3.124
## .Im21 5.139 0.058 87.973 0.000 5.139 3.751
## .Im22 4.278 0.065 65.391 0.000 4.278 2.798
## .Im11 5.653 0.049 115.277 0.000 5.653 4.943
## .Im12 5.666 0.049 116.095 0.000 5.666 4.983
## .Im13 5.448 0.052 105.630 0.000 5.448 4.525
## .Im1 4.792 0.057 84.316 0.000 4.792 3.601
## .Im2 4.861 0.055 88.357 0.000 4.861 3.779
## .Im15 5.090 0.051 99.219 0.000 5.090 4.246
## .Im16 5.130 0.052 98.387 0.000 5.130 4.251
## .Im19 5.146 0.048 106.829 0.000 5.146 4.578
## .Im17 5.025 0.053 94.490 0.000 5.025 4.038
## .Im18 4.595 0.060 76.460 0.000 4.595 3.286
## .Im9 5.075 0.058 87.318 0.000 5.075 3.757
## DECO 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## QUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.215 0.024 8.776 0.000 0.215 0.123
## .Im4 0.108 0.024 4.439 0.000 0.108 0.060
## .Im5 0.744 0.049 15.192 0.000 0.744 0.421
## .Im6 1.030 0.066 15.665 0.000 1.030 0.714
## .Im7 0.867 0.059 14.739 0.000 0.867 0.586
## .Im8 0.482 0.034 14.159 0.000 0.482 0.430
## .Im10 0.127 0.013 9.840 0.000 0.127 0.164
## .Im14 0.101 0.012 8.329 0.000 0.101 0.137
## .Im20 0.629 0.061 10.379 0.000 0.629 0.281
## .Im21 0.721 0.057 12.668 0.000 0.721 0.384
## .Im22 0.554 0.063 8.781 0.000 0.554 0.237
## .Im11 0.814 0.055 14.805 0.000 0.814 0.622
## .Im12 0.310 0.039 7.857 0.000 0.310 0.240
## .Im13 0.390 0.044 8.777 0.000 0.390 0.269
## .Im1 0.253 0.035 7.312 0.000 0.253 0.143
## .Im2 0.308 0.033 9.422 0.000 0.308 0.186
## .Im15 0.651 0.048 13.673 0.000 0.651 0.453
## .Im16 0.968 0.065 14.927 0.000 0.968 0.664
## .Im19 0.820 0.055 14.954 0.000 0.820 0.649
## .Im17 0.146 0.036 4.039 0.000 0.146 0.094
## .Im18 0.482 0.046 10.494 0.000 0.482 0.247
## .Im9 1.415 0.089 15.908 0.000 1.415 0.776
## DECO 1.527 0.107 14.308 0.000 1.000 1.000
## FRENCH 0.412 0.064 6.422 0.000 1.000 1.000
## ATMOS 1.608 0.138 11.683 0.000 1.000 1.000
## QUAL 0.494 0.067 7.365 0.000 1.000 1.000
## CHOICE 1.518 0.110 13.746 0.000 1.000 1.000
## BRAND 1.402 0.100 14.036 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## Im3 NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN
## Im6 NaN 0.286 NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN 0.336 NaN
## Im19 NaN NaN NaN NaN 0.351 NaN
## Im17 NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN 0.224
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1
## FRENCH NaN 1
## ATMOS NaN NaN 1
## QUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
psi## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1.000
## FRENCH 0.434 1.000
## ATMOS 0.466 0.326 1.000
## QUAL 0.471 0.456 0.419 1.000
## CHOICE 0.514 0.378 0.491 0.531 1.000
## BRAND 0.531 0.364 0.528 0.581 0.592 1.000
AVEpsi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO .
## FRENCH NaN .
## ATMOS NaN NaN .
## QUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN -0.011 .
arrange(modificationindices(CFA_fit_img_6f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im1 ~~ Im2 495.934 0.951 0.951 3.408 3.408
## 2 Im10 ~~ Im14 298.631 0.357 0.357 3.154 3.154
## 3 Im6 ~~ Im7 255.917 0.693 0.693 0.734 0.734
## 4 Im16 ~~ Im19 128.231 0.463 0.463 0.519 0.519
## 5 Im7 ~~ Im8 104.366 0.316 0.316 0.489 0.489
## 6 DECO =~ Im19 76.462 0.344 0.424 0.378 0.378
## 7 FRENCH =~ Im9 73.482 0.783 0.503 0.372 0.372
## 8 Im6 ~~ Im10 55.895 -0.158 -0.158 -0.438 -0.438
## 9 Im1 ~~ Im16 55.410 -0.242 -0.242 -0.489 -0.489
## 10 QUAL =~ Im15 54.596 0.510 0.359 0.299 0.299
## 11 Im6 ~~ Im8 52.130 0.236 0.236 0.335 0.335
## 12 Im7 ~~ Im14 50.063 -0.145 -0.145 -0.491 -0.491
## 13 FRENCH =~ Im19 49.872 0.497 0.319 0.284 0.284
## 14 Im15 ~~ Im16 49.062 0.263 0.263 0.332 0.332
## 15 Im1 ~~ Im19 46.763 -0.204 -0.204 -0.449 -0.449
## 16 QUAL =~ Im9 45.834 0.702 0.494 0.365 0.365
## 17 Im2 ~~ Im19 45.384 -0.198 -0.198 -0.393 -0.393
## 18 Im7 ~~ Im9 45.214 0.340 0.340 0.307 0.307
## 19 DECO =~ Im16 44.633 0.288 0.356 0.295 0.295
## 20 BRAND =~ Im19 43.739 0.300 0.355 0.316 0.316
## 21 Im7 ~~ Im10 41.088 -0.134 -0.134 -0.406 -0.406
## 22 QUAL =~ Im2 38.006 -0.361 -0.254 -0.197 -0.197
## 23 BRAND =~ Im15 37.135 0.254 0.301 0.251 0.251
## 24 Im17 ~~ Im18 36.588 0.762 0.762 2.870 2.870
## 25 Im2 ~~ Im15 35.103 -0.179 -0.179 -0.399 -0.399
## 26 Im15 ~~ Im19 34.736 0.202 0.202 0.277 0.277
## 27 QUAL =~ Im19 33.294 0.434 0.305 0.271 0.271
## 28 Im8 ~~ Im14 32.038 -0.103 -0.103 -0.467 -0.467
## 29 Im6 ~~ Im9 31.342 0.301 0.301 0.249 0.249
## 30 Im1 ~~ Im15 30.586 -0.174 -0.174 -0.429 -0.429
## 31 Im2 ~~ Im16 28.333 -0.170 -0.170 -0.311 -0.311
## 32 DECO =~ Im15 27.803 0.191 0.236 0.197 0.197
## 33 Im6 ~~ Im14 27.360 -0.108 -0.108 -0.335 -0.335
## 34 FRENCH =~ Im16 27.263 0.403 0.259 0.214 0.214
## 35 DECO =~ Im2 26.666 -0.158 -0.195 -0.152 -0.152
## 36 ATMOS =~ Im15 24.669 0.181 0.230 0.192 0.192
## 37 BRAND =~ Im13 23.589 0.232 0.275 0.228 0.228
## 38 DECO =~ Im1 22.892 -0.149 -0.184 -0.138 -0.138
## 39 ATMOS =~ Im2 21.308 -0.142 -0.180 -0.140 -0.140
## 40 Im11 ~~ Im13 21.300 -0.191 -0.191 -0.339 -0.339
## 41 BRAND =~ Im2 21.047 -0.165 -0.195 -0.152 -0.152
## 42 FRENCH =~ Im1 20.125 -0.244 -0.156 -0.118 -0.118
## 43 FRENCH =~ Im15 18.582 0.279 0.179 0.149 0.149
## 44 BRAND =~ Im12 18.526 -0.197 -0.233 -0.205 -0.205
## 45 BRAND =~ Im16 17.630 0.209 0.247 0.205 0.205
## 46 BRAND =~ Im1 16.671 -0.150 -0.177 -0.133 -0.133
## 47 ATMOS =~ Im19 16.384 0.161 0.204 0.181 0.181
## 48 BRAND =~ Im6 14.589 0.161 0.191 0.159 0.159
## 49 CHOICE =~ Im20 14.430 -0.169 -0.208 -0.139 -0.139
## 50 Im14 ~~ Im9 13.864 -0.082 -0.082 -0.217 -0.217
## 51 Im11 ~~ Im12 13.374 0.145 0.145 0.289 0.289
## 52 Im21 ~~ Im22 13.217 -0.270 -0.270 -0.427 -0.427
## 53 CHOICE =~ Im13 13.044 0.152 0.187 0.155 0.155
## 54 ATMOS =~ Im7 12.806 0.134 0.170 0.140 0.140
## 55 Im8 ~~ Im10 12.666 -0.065 -0.065 -0.265 -0.265
## 56 FRENCH =~ Im11 12.345 0.269 0.173 0.151 0.151
## 57 CHOICE =~ Im12 11.541 -0.136 -0.168 -0.148 -0.148
## 58 Im3 ~~ Im4 11.447 0.264 0.264 1.735 1.735
## 59 ATMOS =~ Im16 11.243 0.146 0.185 0.153 0.153
## 60 ATMOS =~ Im12 11.072 -0.115 -0.146 -0.128 -0.128
## 61 Im8 ~~ Im9 10.943 0.125 0.125 0.152 0.152
## 62 FRENCH =~ Im2 10.891 -0.177 -0.114 -0.088 -0.088
## 63 Im7 ~~ Im22 10.253 0.126 0.126 0.182 0.182
## 64 DECO =~ Im9 10.194 0.167 0.207 0.153 0.153
## 65 Im11 ~~ Im9 10.067 0.156 0.156 0.145 0.145
## 66 Im15 ~~ Im9 9.926 0.139 0.139 0.145 0.145
## 67 QUAL =~ Im16 9.231 0.250 0.176 0.146 0.146
## 68 Im8 ~~ Im15 9.159 0.080 0.080 0.144 0.144
## 69 ATMOS =~ Im9 9.070 0.162 0.205 0.152 0.152
## 70 Im13 ~~ Im17 9.051 0.067 0.067 0.281 0.281
## 71 Im6 ~~ Im22 8.985 0.125 0.125 0.166 0.166
## 72 Im20 ~~ Im21 8.930 0.206 0.206 0.306 0.306
## 73 BRAND =~ Im22 8.880 0.147 0.175 0.114 0.114
## 74 Im8 ~~ Im16 8.801 0.095 0.095 0.139 0.139
## 75 BRAND =~ Im20 8.486 -0.141 -0.167 -0.111 -0.111
## 76 BRAND =~ Im7 8.244 0.114 0.135 0.111 0.111
## 77 Im3 ~~ Im1 8.143 -0.045 -0.045 -0.194 -0.194
## 78 Im8 ~~ Im2 7.823 -0.059 -0.059 -0.153 -0.153
## 79 QUAL =~ Im18 7.388 -0.230 -0.161 -0.115 -0.115
## 80 Im10 ~~ Im16 7.338 0.052 0.052 0.149 0.149
## 81 Im13 ~~ Im1 7.263 0.060 0.060 0.191 0.191
## 82 Im4 ~~ Im17 7.109 -0.041 -0.041 -0.322 -0.322
## 83 Im22 ~~ Im12 7.028 -0.078 -0.078 -0.189 -0.189
## 84 Im17 ~~ Im9 7.005 -0.112 -0.112 -0.247 -0.247
## 85 DECO =~ Im6 6.969 0.109 0.134 0.112 0.112
## 86 ATMOS =~ Im11 6.857 0.102 0.130 0.113 0.113
## 87 CHOICE =~ Im9 6.692 0.148 0.182 0.135 0.135
## 88 ATMOS =~ Im6 6.616 0.102 0.130 0.108 0.108
## 89 Im14 ~~ Im2 6.285 0.031 0.031 0.175 0.175
## 90 BRAND =~ Im5 6.246 0.103 0.122 0.092 0.092
## 91 BRAND =~ Im4 6.180 -0.071 -0.084 -0.062 -0.062
## 92 Im22 ~~ Im9 5.999 0.121 0.121 0.136 0.136
## 93 QUAL =~ Im5 5.978 0.169 0.119 0.089 0.089
## 94 Im1 ~~ Im9 5.822 -0.084 -0.084 -0.140 -0.140
## 95 QUAL =~ Im1 5.747 -0.143 -0.100 -0.075 -0.075
## 96 CHOICE =~ Im18 5.737 -0.115 -0.141 -0.101 -0.101
## 97 Im3 ~~ Im5 5.693 -0.084 -0.084 -0.209 -0.209
## 98 Im8 ~~ Im22 5.661 0.070 0.070 0.136 0.136
## 99 DECO =~ Im20 5.578 -0.100 -0.123 -0.082 -0.082
## 100 ATMOS =~ Im5 5.473 0.089 0.112 0.084 0.084
## 101 DECO =~ Im17 5.404 -0.091 -0.112 -0.090 -0.090
## 102 Im11 ~~ Im17 5.351 -0.061 -0.061 -0.177 -0.177
## 103 CHOICE =~ Im5 5.052 0.088 0.108 0.082 0.082
## 104 FRENCH =~ Im13 4.802 -0.157 -0.101 -0.084 -0.084
## 105 DECO =~ Im22 4.756 0.094 0.116 0.076 0.076
## 106 Im22 ~~ Im11 4.722 0.083 0.083 0.124 0.124
## 107 CHOICE =~ Im22 4.719 0.099 0.122 0.080 0.080
## 108 Im13 ~~ Im16 4.625 -0.073 -0.073 -0.118 -0.118
## 109 Im19 ~~ Im17 4.621 0.056 0.056 0.161 0.161
## 110 ATMOS =~ Im10 4.609 -0.038 -0.048 -0.055 -0.055
## 111 BRAND =~ Im10 4.570 -0.040 -0.048 -0.054 -0.054
## 112 Im14 ~~ Im22 4.494 -0.036 -0.036 -0.154 -0.154
## 113 ATMOS =~ Im4 4.422 -0.053 -0.067 -0.050 -0.050
## 114 Im14 ~~ Im15 4.415 -0.032 -0.032 -0.127 -0.127
## 115 Im21 ~~ Im9 4.370 -0.102 -0.102 -0.101 -0.101
## 116 Im10 ~~ Im13 4.362 -0.031 -0.031 -0.138 -0.138
## 117 Im7 ~~ Im15 4.358 0.074 0.074 0.098 0.098
## 118 Im3 ~~ Im22 4.300 0.047 0.047 0.135 0.135
## 119 Im20 ~~ Im1 4.283 -0.056 -0.056 -0.141 -0.141
## 120 Im4 ~~ Im16 4.262 0.048 0.048 0.149 0.149
## 121 FRENCH =~ Im5 4.167 0.144 0.093 0.070 0.070
## 122 ATMOS =~ Im8 4.061 0.057 0.072 0.068 0.068
## 123 Im6 ~~ Im20 4.039 -0.084 -0.084 -0.105 -0.105
## 124 Im10 ~~ Im11 4.002 0.036 0.036 0.111 0.111
## 125 Im20 ~~ Im17 3.990 -0.054 -0.054 -0.177 -0.177
## 126 Im6 ~~ Im11 3.977 -0.083 -0.083 -0.091 -0.091
## 127 Im5 ~~ Im1 3.869 0.051 0.051 0.117 0.117
## 128 Im15 ~~ Im17 3.695 0.045 0.045 0.147 0.147
## 129 Im4 ~~ Im18 3.604 0.035 0.035 0.152 0.152
## 130 Im12 ~~ Im15 3.556 0.050 0.050 0.110 0.110
## 131 FRENCH =~ Im17 3.536 -0.115 -0.074 -0.060 -0.060
## 132 Im14 ~~ Im16 3.474 -0.035 -0.035 -0.110 -0.110
## 133 Im3 ~~ Im15 3.381 0.037 0.037 0.099 0.099
## 134 Im3 ~~ Im17 3.375 0.029 0.029 0.161 0.161
## 135 Im3 ~~ Im19 3.371 0.040 0.040 0.096 0.096
## 136 Im13 ~~ Im15 3.338 0.051 0.051 0.102 0.102
## 137 Im22 ~~ Im1 3.275 0.049 0.049 0.132 0.132
## 138 Im20 ~~ Im13 3.270 0.057 0.057 0.115 0.115
## 139 Im13 ~~ Im2 3.219 -0.040 -0.040 -0.116 -0.116
## 140 Im11 ~~ Im1 3.071 -0.047 -0.047 -0.104 -0.104
## 141 CHOICE =~ Im21 3.048 0.074 0.091 0.066 0.066
## 142 Im10 ~~ Im17 3.000 -0.021 -0.021 -0.157 -0.157
## 143 ATMOS =~ Im1 2.962 -0.054 -0.068 -0.051 -0.051
## 144 ATMOS =~ Im13 2.889 0.062 0.078 0.065 0.065
## 145 Im16 ~~ Im9 2.810 0.089 0.089 0.076 0.076
## 146 Im5 ~~ Im14 2.794 0.028 0.028 0.101 0.101
## 147 Im4 ~~ Im22 2.701 -0.036 -0.036 -0.146 -0.146
## 148 CHOICE =~ Im10 2.670 -0.030 -0.037 -0.042 -0.042
## 149 Im1 ~~ Im17 2.662 -0.031 -0.031 -0.161 -0.161
## 150 ATMOS =~ Im14 2.649 -0.028 -0.035 -0.041 -0.041
## 151 Im4 ~~ Im19 2.526 0.034 0.034 0.113 0.113
## 152 Im4 ~~ Im11 2.492 -0.034 -0.034 -0.115 -0.115
## 153 Im21 ~~ Im18 2.456 -0.050 -0.050 -0.086 -0.086
## 154 Im12 ~~ Im2 2.343 -0.032 -0.032 -0.104 -0.104
## 155 Im6 ~~ Im15 2.316 0.057 0.057 0.070 0.070
## 156 Im12 ~~ Im9 2.302 0.057 0.057 0.086 0.086
## 157 DECO =~ Im12 2.287 -0.054 -0.067 -0.059 -0.059
## 158 Im6 ~~ Im1 2.248 -0.044 -0.044 -0.087 -0.087
## 159 Im3 ~~ Im20 2.237 -0.034 -0.034 -0.091 -0.091
## 160 Im15 ~~ Im18 2.236 -0.043 -0.043 -0.077 -0.077
## 161 Im7 ~~ Im1 2.236 -0.042 -0.042 -0.089 -0.089
## 162 Im6 ~~ Im12 2.164 -0.047 -0.047 -0.083 -0.083
## 163 Im10 ~~ Im12 2.160 0.020 0.020 0.102 0.102
## 164 Im4 ~~ Im2 2.090 -0.022 -0.022 -0.123 -0.123
## 165 Im5 ~~ Im6 1.873 -0.055 -0.055 -0.063 -0.063
## 166 Im4 ~~ Im6 1.846 0.032 0.032 0.096 0.096
## 167 DECO =~ Im10 1.832 -0.025 -0.031 -0.035 -0.035
## 168 Im22 ~~ Im2 1.825 -0.037 -0.037 -0.090 -0.090
## 169 Im10 ~~ Im22 1.781 -0.024 -0.024 -0.090 -0.090
## 170 Im12 ~~ Im17 1.776 -0.028 -0.028 -0.131 -0.131
## 171 Im6 ~~ Im18 1.754 0.047 0.047 0.066 0.066
## 172 Im21 ~~ Im17 1.749 0.035 0.035 0.108 0.108
## 173 Im5 ~~ Im16 1.746 -0.052 -0.052 -0.062 -0.062
## 174 Im3 ~~ Im12 1.732 -0.023 -0.023 -0.087 -0.087
## 175 Im22 ~~ Im13 1.726 -0.041 -0.041 -0.089 -0.089
## 176 Im18 ~~ Im9 1.696 -0.060 -0.060 -0.073 -0.073
## 177 ATMOS =~ Im17 1.682 -0.052 -0.065 -0.053 -0.053
## 178 QUAL =~ Im4 1.672 -0.060 -0.042 -0.031 -0.031
## 179 Im20 ~~ Im19 1.649 0.048 0.048 0.067 0.067
## 180 Im20 ~~ Im2 1.631 -0.035 -0.035 -0.080 -0.080
## 181 FRENCH =~ Im18 1.599 -0.082 -0.052 -0.038 -0.038
## 182 Im4 ~~ Im12 1.546 0.021 0.021 0.113 0.113
## 183 CHOICE =~ Im17 1.544 0.057 0.071 0.057 0.057
## 184 Im6 ~~ Im19 1.483 0.050 0.050 0.055 0.055
## 185 Im12 ~~ Im16 1.481 0.038 0.038 0.070 0.070
## 186 Im7 ~~ Im16 1.479 -0.052 -0.052 -0.056 -0.056
## 187 DECO =~ Im13 1.462 0.045 0.056 0.046 0.046
## 188 FRENCH =~ Im20 1.442 -0.089 -0.057 -0.038 -0.038
## 189 Im12 ~~ Im13 1.442 0.089 0.089 0.255 0.255
## 190 BRAND =~ Im3 1.434 0.033 0.039 0.030 0.030
## 191 Im12 ~~ Im1 1.360 -0.024 -0.024 -0.087 -0.087
## 192 Im3 ~~ Im18 1.301 -0.022 -0.022 -0.067 -0.067
## 193 Im16 ~~ Im17 1.269 0.032 0.032 0.085 0.085
## 194 Im3 ~~ Im11 1.261 0.025 0.025 0.060 0.060
## 195 Im14 ~~ Im17 1.252 0.013 0.013 0.110 0.110
## 196 Im10 ~~ Im19 1.233 0.019 0.019 0.060 0.060
## 197 Im3 ~~ Im10 1.230 0.012 0.012 0.070 0.070
## 198 Im8 ~~ Im18 1.200 -0.027 -0.027 -0.057 -0.057
## 199 Im8 ~~ Im1 1.194 -0.023 -0.023 -0.065 -0.065
## 200 Im21 ~~ Im2 1.185 0.030 0.030 0.063 0.063
## 201 QUAL =~ Im22 1.168 -0.084 -0.059 -0.038 -0.038
## 202 CHOICE =~ Im14 1.154 0.019 0.023 0.027 0.027
## 203 Im10 ~~ Im9 1.119 0.024 0.024 0.057 0.057
## 204 DECO =~ Im18 1.115 0.043 0.053 0.038 0.038
## 205 CHOICE =~ Im4 1.111 -0.028 -0.035 -0.026 -0.026
## 206 Im14 ~~ Im21 1.104 0.018 0.018 0.067 0.067
## 207 Im5 ~~ Im19 1.093 -0.038 -0.038 -0.048 -0.048
## 208 Im4 ~~ Im8 1.089 0.017 0.017 0.076 0.076
## 209 Im22 ~~ Im18 1.078 0.034 0.034 0.065 0.065
## 210 Im22 ~~ Im15 1.067 0.036 0.036 0.059 0.059
## 211 Im13 ~~ Im18 1.031 -0.027 -0.027 -0.062 -0.062
## 212 CHOICE =~ Im7 0.941 0.037 0.046 0.038 0.038
## 213 Im4 ~~ Im10 0.906 -0.010 -0.010 -0.082 -0.082
## 214 Im3 ~~ Im14 0.890 -0.010 -0.010 -0.065 -0.065
## 215 Im10 ~~ Im2 0.889 -0.012 -0.012 -0.061 -0.061
## 216 ATMOS =~ Im3 0.869 0.023 0.029 0.022 0.022
## 217 Im11 ~~ Im16 0.846 0.038 0.038 0.043 0.043
## 218 QUAL =~ Im14 0.840 0.031 0.022 0.026 0.026
## 219 QUAL =~ Im20 0.837 0.069 0.049 0.033 0.033
## 220 Im1 ~~ Im18 0.830 0.021 0.021 0.060 0.060
## 221 Im3 ~~ Im16 0.818 0.022 0.022 0.048 0.048
## 222 DECO =~ Im7 0.814 0.035 0.043 0.036 0.036
## 223 Im2 ~~ Im18 0.811 -0.021 -0.021 -0.054 -0.054
## 224 Im20 ~~ Im12 0.794 0.026 0.026 0.059 0.059
## 225 FRENCH =~ Im22 0.781 0.067 0.043 0.028 0.028
## 226 Im20 ~~ Im16 0.767 0.036 0.036 0.046 0.046
## 227 Im14 ~~ Im18 0.739 -0.012 -0.012 -0.056 -0.056
## 228 Im22 ~~ Im19 0.717 -0.032 -0.032 -0.047 -0.047
## 229 QUAL =~ Im10 0.654 -0.028 -0.020 -0.023 -0.023
## 230 Im14 ~~ Im13 0.649 0.011 0.011 0.057 0.057
## 231 Im14 ~~ Im11 0.639 0.014 0.014 0.048 0.048
## 232 CHOICE =~ Im6 0.612 0.032 0.039 0.033 0.033
## 233 Im19 ~~ Im9 0.595 0.037 0.037 0.035 0.035
## 234 BRAND =~ Im11 0.591 -0.036 -0.043 -0.038 -0.038
## 235 Im6 ~~ Im2 0.577 -0.023 -0.023 -0.040 -0.040
## 236 Im20 ~~ Im15 0.576 0.026 0.026 0.041 0.041
## 237 Im5 ~~ Im22 0.561 0.027 0.027 0.043 0.043
## 238 Im8 ~~ Im19 0.558 0.022 0.022 0.035 0.035
## 239 Im8 ~~ Im21 0.538 -0.022 -0.022 -0.037 -0.037
## 240 Im21 ~~ Im12 0.537 0.021 0.021 0.045 0.045
## 241 Im11 ~~ Im19 0.536 0.028 0.028 0.034 0.034
## 242 Im21 ~~ Im1 0.534 0.020 0.020 0.046 0.046
## 243 QUAL =~ Im7 0.517 0.053 0.037 0.031 0.031
## 244 Im10 ~~ Im18 0.516 0.011 0.011 0.044 0.044
## 245 Im5 ~~ Im11 0.511 0.026 0.026 0.034 0.034
## 246 Im10 ~~ Im20 0.483 0.012 0.012 0.044 0.044
## 247 Im12 ~~ Im18 0.465 -0.017 -0.017 -0.044 -0.044
## 248 Im14 ~~ Im1 0.460 0.008 0.008 0.052 0.052
## 249 FRENCH =~ Im3 0.457 -0.031 -0.020 -0.015 -0.015
## 250 Im20 ~~ Im11 0.453 0.026 0.026 0.036 0.036
## 251 Im3 ~~ Im8 0.442 -0.012 -0.012 -0.036 -0.036
## 252 Im20 ~~ Im18 0.417 0.021 0.021 0.038 0.038
## 253 Im20 ~~ Im22 0.407 0.061 0.061 0.103 0.103
## 254 Im10 ~~ Im1 0.405 -0.008 -0.008 -0.045 -0.045
## 255 Im5 ~~ Im20 0.402 0.023 0.023 0.034 0.034
## 256 BRAND =~ Im14 0.390 -0.011 -0.014 -0.016 -0.016
## 257 Im2 ~~ Im9 0.381 -0.022 -0.022 -0.033 -0.033
## 258 Im21 ~~ Im11 0.373 -0.023 -0.023 -0.030 -0.030
## 259 Im16 ~~ Im18 0.357 -0.021 -0.021 -0.030 -0.030
## 260 Im5 ~~ Im15 0.339 -0.019 -0.019 -0.028 -0.028
## 261 Im21 ~~ Im13 0.328 -0.018 -0.018 -0.034 -0.034
## 262 QUAL =~ Im8 0.320 -0.031 -0.022 -0.021 -0.021
## 263 Im5 ~~ Im21 0.319 -0.021 -0.021 -0.028 -0.028
## 264 DECO =~ Im8 0.317 0.016 0.020 0.019 0.019
## 265 Im7 ~~ Im19 0.317 0.022 0.022 0.026 0.026
## 266 Im4 ~~ Im20 0.315 0.012 0.012 0.047 0.047
## 267 Im11 ~~ Im2 0.310 0.015 0.015 0.030 0.030
## 268 Im5 ~~ Im8 0.298 -0.015 -0.015 -0.026 -0.026
## 269 Im7 ~~ Im20 0.292 -0.021 -0.021 -0.029 -0.029
## 270 Im4 ~~ Im13 0.275 -0.009 -0.009 -0.045 -0.045
## 271 Im3 ~~ Im13 0.274 0.010 0.010 0.033 0.033
## 272 Im8 ~~ Im13 0.252 -0.012 -0.012 -0.028 -0.028
## 273 DECO =~ Im11 0.240 0.019 0.024 0.021 0.021
## 274 Im12 ~~ Im19 0.218 0.013 0.013 0.027 0.027
## 275 Im4 ~~ Im5 0.193 0.017 0.017 0.059 0.059
## 276 Im3 ~~ Im7 0.193 -0.010 -0.010 -0.024 -0.024
## 277 Im7 ~~ Im12 0.191 -0.013 -0.013 -0.025 -0.025
## 278 Im5 ~~ Im17 0.190 0.011 0.011 0.033 0.033
## 279 Im7 ~~ Im21 0.188 -0.017 -0.017 -0.022 -0.022
## 280 Im5 ~~ Im9 0.179 0.020 0.020 0.019 0.019
## 281 Im19 ~~ Im18 0.174 -0.013 -0.013 -0.021 -0.021
## 282 Im21 ~~ Im16 0.170 -0.017 -0.017 -0.020 -0.020
## 283 FRENCH =~ Im4 0.152 -0.018 -0.012 -0.009 -0.009
## 284 Im4 ~~ Im15 0.151 -0.008 -0.008 -0.028 -0.028
## 285 Im21 ~~ Im19 0.149 -0.014 -0.014 -0.019 -0.019
## 286 DECO =~ Im14 0.132 -0.007 -0.008 -0.009 -0.009
## 287 Im4 ~~ Im1 0.125 0.005 0.005 0.033 0.033
## 288 Im3 ~~ Im2 0.124 0.006 0.006 0.022 0.022
## 289 Im2 ~~ Im17 0.116 0.006 0.006 0.031 0.031
## 290 Im10 ~~ Im15 0.108 -0.005 -0.005 -0.018 -0.018
## 291 Im5 ~~ Im10 0.106 -0.006 -0.006 -0.018 -0.018
## 292 FRENCH =~ Im21 0.106 0.023 0.015 0.011 0.011
## 293 Im6 ~~ Im16 0.097 -0.014 -0.014 -0.014 -0.014
## 294 CHOICE =~ Im8 0.094 -0.009 -0.011 -0.010 -0.010
## 295 Im7 ~~ Im11 0.091 -0.012 -0.012 -0.014 -0.014
## 296 Im10 ~~ Im21 0.089 -0.005 -0.005 -0.018 -0.018
## 297 Im11 ~~ Im18 0.089 0.010 0.010 0.015 0.015
## 298 Im5 ~~ Im2 0.087 -0.008 -0.008 -0.016 -0.016
## 299 Im7 ~~ Im18 0.086 -0.010 -0.010 -0.015 -0.015
## 300 QUAL =~ Im6 0.086 -0.023 -0.016 -0.013 -0.013
## 301 Im5 ~~ Im12 0.084 0.008 0.008 0.017 0.017
## 302 CHOICE =~ Im11 0.082 -0.012 -0.015 -0.013 -0.013
## 303 Im8 ~~ Im12 0.076 -0.006 -0.006 -0.016 -0.016
## 304 Im6 ~~ Im13 0.071 0.009 0.009 0.014 0.014
## 305 Im14 ~~ Im20 0.068 -0.004 -0.004 -0.018 -0.018
## 306 Im5 ~~ Im7 0.064 0.010 0.010 0.012 0.012
## 307 Im22 ~~ Im17 0.054 0.006 0.006 0.022 0.022
## 308 Im6 ~~ Im21 0.052 -0.010 -0.010 -0.011 -0.011
## 309 QUAL =~ Im21 0.051 0.016 0.011 0.008 0.008
## 310 Im4 ~~ Im21 0.046 0.005 0.005 0.017 0.017
## 311 Im21 ~~ Im15 0.040 -0.007 -0.007 -0.010 -0.010
## 312 Im14 ~~ Im12 0.039 -0.003 -0.003 -0.015 -0.015
## 313 Im7 ~~ Im13 0.037 -0.006 -0.006 -0.011 -0.011
## 314 Im8 ~~ Im17 0.036 -0.004 -0.004 -0.015 -0.015
## 315 QUAL =~ Im17 0.035 -0.015 -0.011 -0.009 -0.009
## 316 BRAND =~ Im21 0.027 -0.007 -0.009 -0.006 -0.006
## 317 Im14 ~~ Im19 0.027 0.003 0.003 0.010 0.010
## 318 Im20 ~~ Im9 0.021 0.007 0.007 0.008 0.008
## 319 Im7 ~~ Im17 0.021 -0.004 -0.004 -0.011 -0.011
## 320 BRAND =~ Im8 0.020 0.004 0.005 0.005 0.005
## 321 CHOICE =~ Im3 0.018 -0.004 -0.004 -0.003 -0.003
## 322 Im3 ~~ Im9 0.018 -0.004 -0.004 -0.007 -0.007
## 323 Im5 ~~ Im18 0.017 0.004 0.004 0.007 0.007
## 324 DECO =~ Im21 0.017 0.005 0.006 0.005 0.005
## 325 Im8 ~~ Im20 0.014 0.003 0.003 0.006 0.006
## 326 Im4 ~~ Im9 0.014 -0.003 -0.003 -0.008 -0.008
## 327 Im3 ~~ Im21 0.010 -0.002 -0.002 -0.006 -0.006
## 328 ATMOS =~ Im18 0.009 0.004 0.005 0.004 0.004
## 329 Im11 ~~ Im15 0.007 -0.003 -0.003 -0.004 -0.004
## 330 Im7 ~~ Im2 0.006 -0.002 -0.002 -0.004 -0.004
## 331 FRENCH =~ Im12 0.002 -0.003 -0.002 -0.002 -0.002
## 332 Im13 ~~ Im9 0.002 0.002 0.002 0.003 0.003
## 333 Im4 ~~ Im14 0.002 0.000 0.000 -0.004 -0.004
## 334 Im4 ~~ Im7 0.002 -0.001 -0.001 -0.003 -0.003
## 335 Im8 ~~ Im11 0.002 0.001 0.001 0.002 0.002
## 336 Im13 ~~ Im19 0.002 0.001 0.001 0.002 0.002
## 337 Im3 ~~ Im6 0.002 0.001 0.001 0.002 0.002
## 338 Im22 ~~ Im16 0.001 0.001 0.001 0.002 0.002
## 339 QUAL =~ Im3 0.001 0.001 0.001 0.001 0.001
## 340 Im6 ~~ Im17 0.000 0.000 0.000 -0.001 -0.001
## 341 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
Based on the modification indices we create a new model
# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "
# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "
CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 85
##
## Number of observations 553
## Number of missing patterns 79
##
## Model Test User Model:
##
## Test statistic 259.047
## Degrees of freedom 124
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 7474.765
## Degrees of freedom 171
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.982
## Tucker-Lewis Index (TLI) 0.975
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.974
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12973.111
## Loglikelihood unrestricted model (H1) -12843.588
##
## Akaike (AIC) 26116.223
## Bayesian (BIC) 26483.028
## Sample-size adjusted Bayesian (SABIC) 26213.200
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.044
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.052
## P-value H_0: RMSEA <= 0.050 0.886
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.045
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.053
## P-value H_0: Robust RMSEA <= 0.050 0.825
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.937
## Im4 1.056 0.025 42.717 0.000 1.305 0.969
## Im5 0.818 0.034 23.815 0.000 1.011 0.760
## FOOD =~
## Im10 1.000 0.812 0.923
## Im14 1.015 0.036 28.479 0.000 0.824 0.952
## ATMOS =~
## Im20 1.000 1.265 0.845
## Im21 0.849 0.041 20.823 0.000 1.074 0.783
## Im22 1.060 0.047 22.606 0.000 1.340 0.877
## PRODQUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.046 0.000 0.991 0.872
## Im13 1.465 0.105 13.968 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.305 0.980
## Im2 0.885 0.033 27.043 0.000 1.155 0.899
## PROF =~
## Im16 1.000 0.921 0.766
## Im19 1.046 0.061 17.170 0.000 0.963 0.856
## BRAND =~
## Im17 1.000 1.204 0.969
## Im18 0.994 0.041 24.143 0.000 1.197 0.856
## FRENCH =~
## Im6 1.000 0.975 0.813
## Im7 1.184 0.071 16.770 0.000 1.155 0.955
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.418 0.050 8.393 0.000 0.416 0.416
## ATMOS 0.730 0.082 8.912 0.000 0.467 0.467
## PRODQUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.711 0.079 9.032 0.000 0.441 0.441
## PROF 0.743 0.071 10.465 0.000 0.653 0.653
## BRAND 0.770 0.076 10.140 0.000 0.517 0.517
## FRENCH 0.402 0.063 6.350 0.000 0.334 0.334
## FOOD ~~
## ATMOS 0.303 0.051 5.948 0.000 0.295 0.295
## PRODQUAL 0.258 0.034 7.662 0.000 0.452 0.452
## CHOICE 0.328 0.050 6.584 0.000 0.309 0.309
## PROF 0.372 0.043 8.589 0.000 0.498 0.498
## BRAND 0.318 0.047 6.801 0.000 0.325 0.325
## FRENCH 0.463 0.047 9.829 0.000 0.585 0.585
## ATMOS ~~
## PRODQUAL 0.372 0.053 7.011 0.000 0.418 0.418
## CHOICE 0.739 0.085 8.728 0.000 0.448 0.448
## PROF 0.557 0.069 8.089 0.000 0.478 0.478
## BRAND 0.787 0.081 9.715 0.000 0.516 0.516
## FRENCH 0.410 0.065 6.352 0.000 0.333 0.333
## PRODQUAL ~~
## CHOICE 0.439 0.054 8.161 0.000 0.478 0.478
## PROF 0.343 0.043 7.946 0.000 0.529 0.529
## BRAND 0.479 0.053 9.046 0.000 0.566 0.566
## FRENCH 0.210 0.037 5.622 0.000 0.306 0.306
## CHOICE ~~
## PROF 0.717 0.072 9.956 0.000 0.597 0.597
## BRAND 0.817 0.079 10.362 0.000 0.519 0.519
## FRENCH 0.286 0.060 4.735 0.000 0.225 0.225
## PROF ~~
## BRAND 0.667 0.066 10.040 0.000 0.601 0.601
## FRENCH 0.328 0.051 6.438 0.000 0.366 0.366
## BRAND ~~
## FRENCH 0.378 0.061 6.175 0.000 0.322 0.322
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.560 0.000 4.995 3.786
## .Im4 4.999 0.057 86.983 0.000 4.999 3.712
## .Im5 5.035 0.057 87.844 0.000 5.035 3.787
## .Im10 6.100 0.037 162.789 0.000 6.100 6.937
## .Im14 6.138 0.037 165.861 0.000 6.138 7.093
## .Im20 4.672 0.064 73.177 0.000 4.672 3.123
## .Im21 5.139 0.058 87.970 0.000 5.139 3.751
## .Im22 4.279 0.065 65.401 0.000 4.279 2.799
## .Im11 5.653 0.049 115.271 0.000 5.653 4.943
## .Im12 5.666 0.049 116.089 0.000 5.666 4.983
## .Im13 5.448 0.052 105.615 0.000 5.448 4.524
## .Im1 4.790 0.057 84.202 0.000 4.790 3.597
## .Im2 4.857 0.055 88.354 0.000 4.857 3.779
## .Im16 5.135 0.052 99.147 0.000 5.135 4.269
## .Im19 5.145 0.048 106.948 0.000 5.145 4.574
## .Im17 5.025 0.053 94.519 0.000 5.025 4.041
## .Im18 4.595 0.060 76.447 0.000 4.595 3.287
## .Im6 5.827 0.051 113.784 0.000 5.827 4.858
## .Im7 5.753 0.052 110.826 0.000 5.753 4.756
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.213 0.024 8.755 0.000 0.213 0.122
## .Im4 0.109 0.024 4.532 0.000 0.109 0.060
## .Im5 0.747 0.049 15.217 0.000 0.747 0.422
## .Im10 0.114 0.019 5.961 0.000 0.114 0.148
## .Im14 0.070 0.019 3.680 0.000 0.070 0.093
## .Im20 0.638 0.061 10.451 0.000 0.638 0.285
## .Im21 0.725 0.057 12.672 0.000 0.725 0.386
## .Im22 0.541 0.063 8.539 0.000 0.541 0.231
## .Im11 0.814 0.055 14.802 0.000 0.814 0.622
## .Im12 0.310 0.040 7.845 0.000 0.310 0.240
## .Im13 0.390 0.045 8.765 0.000 0.390 0.269
## .Im1 0.070 0.050 1.394 0.163 0.070 0.040
## .Im2 0.317 0.044 7.233 0.000 0.317 0.192
## .Im16 0.599 0.052 11.498 0.000 0.599 0.414
## .Im19 0.338 0.045 7.457 0.000 0.338 0.267
## .Im17 0.095 0.045 2.112 0.035 0.095 0.062
## .Im18 0.521 0.055 9.540 0.000 0.521 0.267
## .Im6 0.487 0.056 8.677 0.000 0.487 0.339
## .Im7 0.128 0.067 1.930 0.054 0.128 0.088
## DECO 1.528 0.107 14.326 0.000 1.000 1.000
## FOOD 0.659 0.049 13.328 0.000 1.000 1.000
## ATMOS 1.599 0.138 11.623 0.000 1.000 1.000
## PRODQUAL 0.494 0.067 7.361 0.000 1.000 1.000
## CHOICE 1.704 0.118 14.388 0.000 1.000 1.000
## PROF 0.849 0.088 9.638 0.000 1.000 1.000
## BRAND 1.451 0.104 13.988 0.000 1.000 1.000
## FRENCH 0.952 0.095 10.058 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1
## FOOD NaN 1
## ATMOS NaN NaN 1
## PRODQUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## PROF NaN NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN NaN 1
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH
## DECO 0.786707
## FOOD 0.786707
## ATMOS 0.786707
## PRODQUAL 0.786707
## CHOICE 0.786707
## PROF 0.786707
## BRAND 0.786707
## FRENCH 0.786707
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1.000
## FOOD 0.416 1.000
## ATMOS 0.467 0.295 1.000
## PRODQUAL 0.471 0.452 0.418 1.000
## CHOICE 0.441 0.309 0.448 0.478 1.000
## PROF 0.653 0.498 0.478 0.529 0.597 1.000
## BRAND 0.517 0.325 0.516 0.566 0.519 0.601 1.000
## FRENCH 0.334 0.585 0.333 0.306 0.225 0.366 0.322 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
arrange(modificationindices(CFA_fit_img_7f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 BRAND =~ Im13 23.832 0.220 0.265 0.220 0.220
## 2 Im11 ~~ Im13 21.323 -0.191 -0.191 -0.338 -0.338
## 3 BRAND =~ Im12 17.245 -0.179 -0.216 -0.190 -0.190
## 4 Im21 ~~ Im22 15.139 -0.285 -0.285 -0.455 -0.455
## 5 CHOICE =~ Im20 14.777 -0.151 -0.197 -0.132 -0.132
## 6 CHOICE =~ Im13 13.970 0.133 0.174 0.144 0.144
## 7 Im11 ~~ Im12 13.307 0.145 0.145 0.288 0.288
## 8 FOOD =~ Im11 12.742 0.215 0.174 0.152 0.152
## 9 Im20 ~~ Im21 11.455 0.228 0.228 0.335 0.335
## 10 ATMOS =~ Im12 10.952 -0.115 -0.145 -0.127 -0.127
## 11 Im13 ~~ Im1 10.707 0.068 0.068 0.409 0.409
## 12 CHOICE =~ Im12 10.663 -0.111 -0.145 -0.127 -0.127
## 13 Im13 ~~ Im17 9.392 0.068 0.068 0.355 0.355
## 14 Im4 ~~ Im17 9.096 -0.046 -0.046 -0.446 -0.446
## 15 BRAND =~ Im20 8.230 -0.133 -0.160 -0.107 -0.107
## 16 Im10 ~~ Im16 7.956 0.046 0.046 0.175 0.175
## 17 BRAND =~ Im22 7.656 0.131 0.158 0.103 0.103
## 18 FRENCH =~ Im22 7.278 0.136 0.132 0.087 0.087
## 19 ATMOS =~ Im11 6.691 0.101 0.128 0.112 0.112
## 20 Im22 ~~ Im12 6.644 -0.076 -0.076 -0.185 -0.185
## 21 CHOICE =~ Im5 6.302 0.086 0.112 0.084 0.084
## 22 BRAND =~ Im4 6.247 -0.067 -0.081 -0.060 -0.060
## 23 PRODQUAL =~ Im5 6.120 0.171 0.120 0.091 0.091
## 24 Im14 ~~ Im16 6.048 -0.039 -0.039 -0.191 -0.191
## 25 Im10 ~~ Im6 6.011 -0.035 -0.035 -0.147 -0.147
## 26 BRAND =~ Im5 5.755 0.095 0.115 0.086 0.086
## 27 Im3 ~~ Im1 5.614 -0.034 -0.034 -0.281 -0.281
## 28 DECO =~ Im7 5.531 -0.093 -0.114 -0.095 -0.095
## 29 DECO =~ Im6 5.531 0.078 0.097 0.080 0.080
## 30 ATMOS =~ Im5 5.517 0.089 0.113 0.085 0.085
## 31 DECO =~ Im18 5.361 0.099 0.123 0.088 0.088
## 32 DECO =~ Im17 5.361 -0.100 -0.124 -0.099 -0.099
## 33 FRENCH =~ Im20 5.231 -0.113 -0.111 -0.074 -0.074
## 34 Im22 ~~ Im11 5.182 0.087 0.087 0.131 0.131
## 35 FOOD =~ Im13 5.137 -0.127 -0.103 -0.086 -0.086
## 36 Im3 ~~ Im4 5.131 0.162 0.162 1.061 1.061
## 37 DECO =~ Im20 5.124 -0.096 -0.118 -0.079 -0.079
## 38 BRAND =~ Im7 5.064 -0.090 -0.108 -0.089 -0.089
## 39 BRAND =~ Im6 5.064 0.076 0.091 0.076 0.076
## 40 Im22 ~~ Im1 5.051 0.056 0.056 0.290 0.290
## 41 Im13 ~~ Im16 5.040 -0.067 -0.067 -0.138 -0.138
## 42 Im11 ~~ Im6 4.965 -0.069 -0.069 -0.109 -0.109
## 43 Im10 ~~ Im13 4.793 -0.031 -0.031 -0.146 -0.146
## 44 Im4 ~~ Im18 4.776 0.040 0.040 0.166 0.166
## 45 Im5 ~~ Im6 4.758 -0.065 -0.065 -0.108 -0.108
## 46 Im3 ~~ Im22 4.749 0.049 0.049 0.143 0.143
## 47 Im10 ~~ Im7 4.706 0.032 0.032 0.265 0.265
## 48 CHOICE =~ Im22 4.697 0.087 0.113 0.074 0.074
## 49 Im3 ~~ Im5 4.674 -0.071 -0.071 -0.178 -0.178
## 50 Im13 ~~ Im2 4.562 -0.044 -0.044 -0.125 -0.125
## 51 FOOD =~ Im5 4.520 0.117 0.095 0.072 0.072
## 52 Im20 ~~ Im17 4.488 -0.057 -0.057 -0.230 -0.230
## 53 ATMOS =~ Im4 4.309 -0.052 -0.066 -0.049 -0.049
## 54 DECO =~ Im22 4.302 0.090 0.111 0.072 0.072
## 55 PROF =~ Im2 4.223 0.170 0.157 0.122 0.122
## 56 PROF =~ Im1 4.223 -0.192 -0.177 -0.133 -0.133
## 57 Im20 ~~ Im6 4.215 -0.064 -0.064 -0.115 -0.115
## 58 PRODQUAL =~ Im1 4.027 0.145 0.102 0.077 0.077
## 59 PRODQUAL =~ Im2 4.027 -0.129 -0.090 -0.070 -0.070
## 60 PROF =~ Im12 3.965 -0.117 -0.108 -0.095 -0.095
## 61 Im14 ~~ Im6 3.823 0.027 0.027 0.149 0.149
## 62 FOOD =~ Im6 3.804 -0.271 -0.220 -0.183 -0.183
## 63 FOOD =~ Im7 3.804 0.321 0.260 0.215 0.215
## 64 Im2 ~~ Im17 3.691 0.033 0.033 0.192 0.192
## 65 Im4 ~~ Im6 3.588 0.033 0.033 0.143 0.143
## 66 Im3 ~~ Im17 3.342 0.028 0.028 0.198 0.198
## 67 Im11 ~~ Im1 3.335 -0.045 -0.045 -0.189 -0.189
## 68 Im5 ~~ Im1 3.275 0.043 0.043 0.188 0.188
## 69 PROF =~ Im20 3.209 -0.113 -0.104 -0.069 -0.069
## 70 CHOICE =~ Im21 3.202 0.067 0.087 0.064 0.064
## 71 Im3 ~~ Im2 3.151 0.026 0.026 0.100 0.100
## 72 Im20 ~~ Im13 3.089 0.055 0.055 0.111 0.111
## 73 Im18 ~~ Im6 3.067 0.046 0.046 0.091 0.091
## 74 Im14 ~~ Im7 3.014 -0.026 -0.026 -0.272 -0.272
## 75 Im11 ~~ Im17 2.983 -0.045 -0.045 -0.163 -0.163
## 76 FRENCH =~ Im11 2.967 0.080 0.078 0.069 0.069
## 77 ATMOS =~ Im13 2.904 0.062 0.078 0.065 0.065
## 78 Im5 ~~ Im7 2.807 0.048 0.048 0.154 0.154
## 79 Im10 ~~ Im11 2.784 0.028 0.028 0.093 0.093
## 80 Im20 ~~ Im1 2.774 -0.042 -0.042 -0.198 -0.198
## 81 Im5 ~~ Im14 2.721 0.026 0.026 0.115 0.115
## 82 Im1 ~~ Im17 2.656 -0.029 -0.029 -0.359 -0.359
## 83 FRENCH =~ Im19 2.578 0.085 0.083 0.074 0.074
## 84 FRENCH =~ Im16 2.578 -0.082 -0.080 -0.066 -0.066
## 85 Im2 ~~ Im16 2.577 0.038 0.038 0.088 0.088
## 86 CHOICE =~ Im14 2.577 0.027 0.035 0.041 0.041
## 87 CHOICE =~ Im10 2.577 -0.026 -0.035 -0.039 -0.039
## 88 Im21 ~~ Im18 2.573 -0.052 -0.052 -0.084 -0.084
## 89 Im4 ~~ Im11 2.457 -0.034 -0.034 -0.113 -0.113
## 90 PROF =~ Im13 2.455 0.096 0.089 0.074 0.074
## 91 Im22 ~~ Im19 2.419 -0.049 -0.049 -0.115 -0.115
## 92 Im4 ~~ Im22 2.418 -0.034 -0.034 -0.138 -0.138
## 93 Im3 ~~ Im20 2.350 -0.034 -0.034 -0.093 -0.093
## 94 Im12 ~~ Im7 2.333 0.036 0.036 0.178 0.178
## 95 DECO =~ Im12 2.244 -0.054 -0.066 -0.058 -0.058
## 96 Im11 ~~ Im7 2.221 0.044 0.044 0.137 0.137
## 97 Im19 ~~ Im17 2.187 0.035 0.035 0.193 0.193
## 98 PRODQUAL =~ Im16 2.157 -0.133 -0.094 -0.078 -0.078
## 99 PRODQUAL =~ Im19 2.157 0.140 0.098 0.087 0.087
## 100 Im10 ~~ Im17 2.035 -0.017 -0.017 -0.161 -0.161
## 101 Im14 ~~ Im17 1.988 0.016 0.016 0.201 0.201
## 102 Im4 ~~ Im1 1.978 0.020 0.020 0.227 0.227
## 103 Im3 ~~ Im12 1.906 -0.024 -0.024 -0.092 -0.092
## 104 Im12 ~~ Im6 1.902 -0.033 -0.033 -0.084 -0.084
## 105 CHOICE =~ Im16 1.817 0.068 0.089 0.074 0.074
## 106 CHOICE =~ Im19 1.817 -0.071 -0.093 -0.083 -0.083
## 107 Im14 ~~ Im2 1.800 0.015 0.015 0.098 0.098
## 108 Im18 ~~ Im7 1.743 -0.033 -0.033 -0.128 -0.128
## 109 FRENCH =~ Im5 1.735 0.059 0.057 0.043 0.043
## 110 Im11 ~~ Im2 1.713 0.033 0.033 0.064 0.064
## 111 ATMOS =~ Im17 1.684 -0.057 -0.073 -0.058 -0.058
## 112 ATMOS =~ Im18 1.684 0.057 0.072 0.052 0.052
## 113 Im19 ~~ Im18 1.680 -0.034 -0.034 -0.082 -0.082
## 114 BRAND =~ Im3 1.663 0.034 0.041 0.031 0.031
## 115 Im3 ~~ Im14 1.662 -0.012 -0.012 -0.102 -0.102
## 116 FRENCH =~ Im2 1.647 0.039 0.038 0.030 0.030
## 117 FRENCH =~ Im1 1.647 -0.045 -0.043 -0.033 -0.033
## 118 Im22 ~~ Im2 1.646 -0.032 -0.032 -0.077 -0.077
## 119 Im22 ~~ Im18 1.613 0.041 0.041 0.077 0.077
## 120 FOOD =~ Im2 1.604 0.050 0.040 0.031 0.031
## 121 FOOD =~ Im1 1.604 -0.056 -0.046 -0.034 -0.034
## 122 PRODQUAL =~ Im4 1.602 -0.058 -0.041 -0.030 -0.030
## 123 Im22 ~~ Im13 1.588 -0.040 -0.040 -0.086 -0.086
## 124 Im4 ~~ Im2 1.557 -0.018 -0.018 -0.095 -0.095
## 125 Im14 ~~ Im21 1.552 0.021 0.021 0.091 0.091
## 126 Im5 ~~ Im16 1.529 -0.043 -0.043 -0.064 -0.064
## 127 Im12 ~~ Im17 1.526 -0.026 -0.026 -0.151 -0.151
## 128 Im10 ~~ Im18 1.519 0.018 0.018 0.072 0.072
## 129 PRODQUAL =~ Im22 1.519 -0.095 -0.067 -0.044 -0.044
## 130 Im2 ~~ Im18 1.481 -0.026 -0.026 -0.063 -0.063
## 131 Im12 ~~ Im13 1.475 0.089 0.089 0.257 0.257
## 132 PRODQUAL =~ Im6 1.473 -0.073 -0.052 -0.043 -0.043
## 133 PRODQUAL =~ Im7 1.473 0.087 0.061 0.051 0.051
## 134 Im14 ~~ Im18 1.464 -0.017 -0.017 -0.088 -0.088
## 135 PROF =~ Im22 1.445 0.077 0.071 0.047 0.047
## 136 DECO =~ Im13 1.431 0.045 0.055 0.046 0.046
## 137 PRODQUAL =~ Im17 1.422 0.109 0.076 0.062 0.062
## 138 PRODQUAL =~ Im18 1.422 -0.108 -0.076 -0.054 -0.054
## 139 Im4 ~~ Im12 1.373 0.019 0.019 0.106 0.106
## 140 ATMOS =~ Im1 1.355 0.043 0.054 0.040 0.040
## 141 ATMOS =~ Im2 1.355 -0.038 -0.048 -0.037 -0.037
## 142 Im22 ~~ Im7 1.342 0.035 0.035 0.133 0.133
## 143 Im3 ~~ Im18 1.316 -0.022 -0.022 -0.065 -0.065
## 144 Im3 ~~ Im11 1.290 0.025 0.025 0.061 0.061
## 145 PROF =~ Im4 1.267 -0.055 -0.050 -0.037 -0.037
## 146 Im13 ~~ Im19 1.244 0.029 0.029 0.080 0.080
## 147 Im3 ~~ Im10 1.231 0.011 0.011 0.071 0.071
## 148 Im10 ~~ Im12 1.205 0.014 0.014 0.077 0.077
## 149 Im12 ~~ Im16 1.199 0.030 0.030 0.071 0.071
## 150 BRAND =~ Im11 1.070 -0.047 -0.056 -0.049 -0.049
## 151 BRAND =~ Im2 1.067 0.042 0.051 0.039 0.039
## 152 BRAND =~ Im1 1.067 -0.048 -0.057 -0.043 -0.043
## 153 Im14 ~~ Im12 1.061 -0.013 -0.013 -0.090 -0.090
## 154 Im4 ~~ Im7 1.054 -0.017 -0.017 -0.147 -0.147
## 155 PRODQUAL =~ Im20 1.037 0.077 0.054 0.036 0.036
## 156 Im21 ~~ Im17 1.017 0.027 0.027 0.101 0.101
## 157 Im20 ~~ Im19 0.988 0.031 0.031 0.068 0.068
## 158 PROF =~ Im17 0.986 0.084 0.077 0.062 0.062
## 159 PROF =~ Im18 0.986 -0.083 -0.077 -0.055 -0.055
## 160 Im19 ~~ Im7 0.949 0.025 0.025 0.122 0.122
## 161 PROF =~ Im7 0.940 -0.060 -0.055 -0.045 -0.045
## 162 PROF =~ Im6 0.940 0.050 0.046 0.039 0.039
## 163 Im13 ~~ Im18 0.925 -0.026 -0.026 -0.057 -0.057
## 164 Im5 ~~ Im2 0.918 -0.023 -0.023 -0.047 -0.047
## 165 Im14 ~~ Im13 0.889 0.013 0.013 0.079 0.079
## 166 Im16 ~~ Im7 0.880 -0.027 -0.027 -0.097 -0.097
## 167 Im1 ~~ Im18 0.847 0.019 0.019 0.101 0.101
## 168 ATMOS =~ Im3 0.826 0.022 0.028 0.022 0.022
## 169 FOOD =~ Im20 0.814 -0.052 -0.042 -0.028 -0.028
## 170 Im22 ~~ Im6 0.806 0.028 0.028 0.054 0.054
## 171 Im5 ~~ Im19 0.786 -0.026 -0.026 -0.052 -0.052
## 172 BRAND =~ Im16 0.775 -0.050 -0.060 -0.050 -0.050
## 173 BRAND =~ Im19 0.775 0.052 0.063 0.056 0.056
## 174 Im3 ~~ Im19 0.774 0.016 0.016 0.061 0.061
## 175 BRAND =~ Im14 0.773 0.017 0.020 0.023 0.023
## 176 BRAND =~ Im10 0.773 -0.016 -0.020 -0.022 -0.022
## 177 Im10 ~~ Im19 0.726 -0.012 -0.012 -0.062 -0.062
## 178 FRENCH =~ Im13 0.706 -0.035 -0.034 -0.028 -0.028
## 179 PROF =~ Im5 0.688 0.055 0.051 0.038 0.038
## 180 Im4 ~~ Im5 0.687 0.029 0.029 0.103 0.103
## 181 Im20 ~~ Im12 0.675 0.024 0.024 0.054 0.054
## 182 Im2 ~~ Im7 0.669 0.016 0.016 0.079 0.079
## 183 Im3 ~~ Im7 0.637 -0.014 -0.014 -0.084 -0.084
## 184 PRODQUAL =~ Im14 0.619 0.031 0.022 0.025 0.025
## 185 PRODQUAL =~ Im10 0.619 -0.030 -0.021 -0.024 -0.024
## 186 Im21 ~~ Im7 0.611 -0.023 -0.023 -0.076 -0.076
## 187 Im5 ~~ Im22 0.596 0.028 0.028 0.044 0.044
## 188 Im4 ~~ Im10 0.595 -0.007 -0.007 -0.066 -0.066
## 189 Im20 ~~ Im18 0.582 0.025 0.025 0.043 0.043
## 190 Im10 ~~ Im2 0.581 -0.008 -0.008 -0.045 -0.045
## 191 Im4 ~~ Im16 0.579 0.016 0.016 0.062 0.062
## 192 Im21 ~~ Im2 0.574 0.019 0.019 0.039 0.039
## 193 Im10 ~~ Im21 0.544 -0.013 -0.013 -0.043 -0.043
## 194 Im14 ~~ Im22 0.525 -0.012 -0.012 -0.062 -0.062
## 195 Im13 ~~ Im7 0.518 -0.018 -0.018 -0.080 -0.080
## 196 Im5 ~~ Im11 0.501 0.026 0.026 0.033 0.033
## 197 Im20 ~~ Im11 0.498 0.027 0.027 0.038 0.038
## 198 Im12 ~~ Im2 0.492 -0.013 -0.013 -0.043 -0.043
## 199 Im11 ~~ Im18 0.492 0.023 0.023 0.035 0.035
## 200 CHOICE =~ Im3 0.483 -0.015 -0.020 -0.015 -0.015
## 201 Im1 ~~ Im16 0.483 -0.017 -0.017 -0.082 -0.082
## 202 Im21 ~~ Im12 0.479 0.020 0.020 0.043 0.043
## 203 Im5 ~~ Im10 0.474 -0.011 -0.011 -0.039 -0.039
## 204 CHOICE =~ Im11 0.473 -0.026 -0.034 -0.030 -0.030
## 205 Im10 ~~ Im20 0.466 0.012 0.012 0.043 0.043
## 206 PROF =~ Im3 0.453 0.032 0.029 0.022 0.022
## 207 FRENCH =~ Im3 0.431 -0.019 -0.018 -0.014 -0.014
## 208 FOOD =~ Im3 0.430 -0.023 -0.019 -0.014 -0.014
## 209 FOOD =~ Im19 0.429 0.047 0.038 0.034 0.034
## 210 FOOD =~ Im16 0.429 -0.045 -0.037 -0.031 -0.031
## 211 PROF =~ Im11 0.410 0.039 0.036 0.032 0.032
## 212 Im5 ~~ Im20 0.382 0.023 0.023 0.033 0.033
## 213 Im13 ~~ Im6 0.377 0.016 0.016 0.036 0.036
## 214 Im14 ~~ Im19 0.372 0.009 0.009 0.056 0.056
## 215 Im21 ~~ Im13 0.372 -0.019 -0.019 -0.036 -0.036
## 216 PROF =~ Im21 0.371 0.036 0.033 0.024 0.024
## 217 CHOICE =~ Im4 0.369 -0.014 -0.018 -0.013 -0.013
## 218 Im22 ~~ Im17 0.360 0.016 0.016 0.071 0.071
## 219 FRENCH =~ Im21 0.360 -0.029 -0.028 -0.020 -0.020
## 220 Im21 ~~ Im11 0.346 -0.022 -0.022 -0.029 -0.029
## 221 Im5 ~~ Im17 0.345 0.015 0.015 0.055 0.055
## 222 Im14 ~~ Im20 0.330 -0.010 -0.010 -0.045 -0.045
## 223 FOOD =~ Im21 0.320 0.032 0.026 0.019 0.019
## 224 CHOICE =~ Im17 0.309 0.023 0.030 0.024 0.024
## 225 CHOICE =~ Im18 0.309 -0.023 -0.030 -0.021 -0.021
## 226 Im3 ~~ Im13 0.299 0.010 0.010 0.035 0.035
## 227 Im4 ~~ Im19 0.281 -0.010 -0.010 -0.050 -0.050
## 228 Im22 ~~ Im16 0.277 0.019 0.019 0.033 0.033
## 229 Im5 ~~ Im21 0.277 -0.019 -0.019 -0.026 -0.026
## 230 Im4 ~~ Im14 0.246 0.005 0.005 0.053 0.053
## 231 DECO =~ Im11 0.238 0.019 0.024 0.021 0.021
## 232 Im16 ~~ Im18 0.231 -0.015 -0.015 -0.026 -0.026
## 233 Im17 ~~ Im7 0.228 -0.010 -0.010 -0.094 -0.094
## 234 Im21 ~~ Im16 0.227 -0.017 -0.017 -0.026 -0.026
## 235 Im20 ~~ Im22 0.211 0.043 0.043 0.074 0.074
## 236 Im17 ~~ Im6 0.208 0.010 0.010 0.045 0.045
## 237 Im20 ~~ Im2 0.203 -0.011 -0.011 -0.025 -0.025
## 238 Im2 ~~ Im19 0.202 -0.009 -0.009 -0.029 -0.029
## 239 FOOD =~ Im4 0.194 -0.016 -0.013 -0.010 -0.010
## 240 Im4 ~~ Im13 0.168 -0.007 -0.007 -0.035 -0.035
## 241 Im14 ~~ Im11 0.165 0.007 0.007 0.028 0.028
## 242 FOOD =~ Im22 0.151 0.023 0.018 0.012 0.012
## 243 Im12 ~~ Im18 0.146 -0.010 -0.010 -0.024 -0.024
## 244 Im20 ~~ Im16 0.145 0.014 0.014 0.022 0.022
## 245 Im21 ~~ Im1 0.132 0.009 0.009 0.040 0.040
## 246 ATMOS =~ Im19 0.131 -0.017 -0.022 -0.019 -0.019
## 247 ATMOS =~ Im16 0.131 0.016 0.021 0.017 0.017
## 248 Im4 ~~ Im20 0.129 0.008 0.008 0.029 0.029
## 249 Im1 ~~ Im7 0.126 -0.007 -0.007 -0.075 -0.075
## 250 Im12 ~~ Im1 0.110 -0.006 -0.006 -0.044 -0.044
## 251 Im3 ~~ Im6 0.106 0.006 0.006 0.018 0.018
## 252 Im2 ~~ Im6 0.094 -0.006 -0.006 -0.016 -0.016
## 253 FRENCH =~ Im18 0.094 0.013 0.012 0.009 0.009
## 254 FRENCH =~ Im17 0.094 -0.013 -0.013 -0.010 -0.010
## 255 Im10 ~~ Im1 0.093 -0.003 -0.003 -0.038 -0.038
## 256 PRODQUAL =~ Im21 0.088 0.021 0.015 0.011 0.011
## 257 Im5 ~~ Im18 0.083 0.009 0.009 0.014 0.014
## 258 Im20 ~~ Im7 0.082 0.009 0.009 0.030 0.030
## 259 DECO =~ Im2 0.075 0.009 0.011 0.008 0.008
## 260 DECO =~ Im1 0.075 -0.010 -0.012 -0.009 -0.009
## 261 Im5 ~~ Im12 0.067 0.007 0.007 0.015 0.015
## 262 Im14 ~~ Im1 0.063 -0.003 -0.003 -0.039 -0.039
## 263 ATMOS =~ Im14 0.061 0.004 0.006 0.006 0.006
## 264 ATMOS =~ Im10 0.061 -0.004 -0.006 -0.006 -0.006
## 265 Im21 ~~ Im19 0.060 0.008 0.008 0.015 0.015
## 266 Im4 ~~ Im21 0.059 0.005 0.005 0.018 0.018
## 267 PROF =~ Im10 0.058 0.008 0.007 0.008 0.008
## 268 PROF =~ Im14 0.058 -0.008 -0.007 -0.009 -0.009
## 269 Im1 ~~ Im19 0.056 -0.005 -0.005 -0.034 -0.034
## 270 CHOICE =~ Im6 0.055 -0.007 -0.009 -0.007 -0.007
## 271 CHOICE =~ Im7 0.055 0.008 0.010 0.008 0.008
## 272 DECO =~ Im14 0.052 0.005 0.006 0.007 0.007
## 273 DECO =~ Im10 0.052 -0.005 -0.006 -0.006 -0.006
## 274 Im10 ~~ Im22 0.051 0.004 0.004 0.015 0.015
## 275 FRENCH =~ Im12 0.045 -0.008 -0.008 -0.007 -0.007
## 276 Im1 ~~ Im6 0.039 -0.004 -0.004 -0.021 -0.021
## 277 ATMOS =~ Im6 0.036 -0.006 -0.008 -0.007 -0.007
## 278 ATMOS =~ Im7 0.036 0.008 0.010 0.008 0.008
## 279 Im12 ~~ Im19 0.023 -0.004 -0.004 -0.011 -0.011
## 280 DECO =~ Im21 0.016 0.005 0.006 0.005 0.005
## 281 FOOD =~ Im17 0.015 0.006 0.005 0.004 0.004
## 282 FOOD =~ Im18 0.015 -0.006 -0.005 -0.004 -0.004
## 283 Im3 ~~ Im21 0.013 -0.003 -0.003 -0.006 -0.006
## 284 Im16 ~~ Im6 0.011 -0.003 -0.003 -0.006 -0.006
## 285 Im19 ~~ Im6 0.009 -0.002 -0.002 -0.006 -0.006
## 286 Im11 ~~ Im19 0.006 -0.002 -0.002 -0.005 -0.005
## 287 Im21 ~~ Im6 0.006 0.002 0.002 0.004 0.004
## 288 DECO =~ Im16 0.004 0.004 0.005 0.004 0.004
## 289 DECO =~ Im19 0.004 -0.004 -0.005 -0.004 -0.004
## 290 Im11 ~~ Im16 0.002 0.002 0.002 0.002 0.002
## 291 FRENCH =~ Im14 0.001 0.001 0.001 0.002 0.002
## 292 FRENCH =~ Im10 0.001 -0.001 -0.001 -0.002 -0.002
## 293 Im3 ~~ Im16 0.001 -0.001 -0.001 -0.002 -0.002
## 294 FRENCH =~ Im4 0.001 -0.001 -0.001 0.000 0.000
## 295 Im16 ~~ Im17 0.000 0.000 0.000 0.002 0.002
## 296 PRODQUAL =~ Im3 0.000 0.000 0.000 0.000 0.000
## 297 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
## 298 BRAND =~ Im21 0.000 0.000 0.000 0.000 0.000
## 299 FOOD =~ Im12 0.000 0.000 0.000 0.000 0.000
## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
#
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
#
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
#
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
#
# CFA_data# missing Im8, Im15, Im9
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "
# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4
SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
"# # linear regression
# lm_SAT_1 <- lm (model_SAT_1, data = survey)
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 143 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 148
##
## Number of observations 553
## Number of missing patterns 135
##
## Model Test User Model:
##
## Test statistic 807.817
## Degrees of freedom 412
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 11978.557
## Degrees of freedom 496
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.966
## Tucker-Lewis Index (TLI) 0.959
##
## Robust Comparative Fit Index (CFI) 0.966
## Robust Tucker-Lewis Index (TLI) 0.959
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -22422.581
## Loglikelihood unrestricted model (H1) -22018.673
##
## Akaike (AIC) 45141.162
## Bayesian (BIC) 45779.835
## Sample-size adjusted Bayesian (SABIC) 45310.018
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.042
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.046
## P-value H_0: RMSEA <= 0.050 0.999
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.042
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.047
## P-value H_0: Robust RMSEA <= 0.050 0.998
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.059
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.235 0.936
## Im4 1.057 0.025 42.676 0.000 1.306 0.970
## Im5 0.818 0.034 23.801 0.000 1.010 0.760
## FOOD =~
## Im10 1.000 0.810 0.921
## Im14 1.019 0.036 28.596 0.000 0.826 0.954
## ATMOS =~
## Im20 1.000 1.253 0.838
## Im21 0.865 0.041 20.940 0.000 1.084 0.791
## Im22 1.060 0.046 23.188 0.000 1.327 0.869
## PRODQUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.409 0.094 15.045 0.000 0.991 0.872
## Im13 1.464 0.105 13.957 0.000 1.029 0.855
## CHOICE =~
## Im1 1.000 1.302 0.978
## Im2 0.889 0.032 27.907 0.000 1.157 0.900
## PROF =~
## Im16 1.000 0.911 0.757
## Im19 1.030 0.056 18.278 0.000 0.938 0.834
## BRAND =~
## Im17 1.000 1.205 0.970
## Im18 0.992 0.041 24.147 0.000 1.196 0.856
## FRENCH =~
## Im6 1.000 0.986 0.822
## Im7 1.161 0.066 17.619 0.000 1.144 0.945
## AFCOM =~
## COM_A1 1.000 1.120 0.785
## COM_A2 1.180 0.056 21.211 0.000 1.321 0.830
## COM_A3 1.176 0.059 19.829 0.000 1.317 0.816
## COM_A4 1.297 0.063 20.613 0.000 1.453 0.845
## SAT =~
## SAT_1 1.000 0.868 0.859
## SAT_2 0.937 0.049 19.036 0.000 0.814 0.818
## SAT_3 0.812 0.055 14.799 0.000 0.705 0.620
## RI =~
## C_REP1 1.000 0.588 0.798
## C_REP2 1.021 0.047 21.905 0.000 0.601 0.955
## C_REP3 0.719 0.038 19.135 0.000 0.423 0.758
## COI =~
## C_CR1 1.000 1.641 0.848
## C_CR3 1.033 0.051 20.134 0.000 1.695 0.822
## C_CR4 0.967 0.049 19.687 0.000 1.587 0.805
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SAT ~
## DECO -0.107 0.046 -2.357 0.018 -0.153 -0.153
## CHOICE 0.095 0.040 2.379 0.017 0.142 0.142
## PROF 0.615 0.090 6.808 0.000 0.645 0.645
## AFCOM ~
## ATMOS 0.437 0.047 9.282 0.000 0.489 0.489
## PRODQUAL -0.037 0.076 -0.485 0.628 -0.023 -0.023
## FRENCH 0.206 0.051 4.031 0.000 0.182 0.182
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.416 0.050 8.380 0.000 0.416 0.416
## ATMOS 0.730 0.081 8.972 0.000 0.472 0.472
## PRODQUAL 0.408 0.051 8.031 0.000 0.470 0.470
## CHOICE 0.709 0.079 9.024 0.000 0.441 0.441
## PROF 0.750 0.070 10.690 0.000 0.667 0.667
## BRAND 0.768 0.076 10.124 0.000 0.516 0.516
## FRENCH 0.412 0.063 6.494 0.000 0.338 0.338
## RI 0.181 0.035 5.193 0.000 0.249 0.249
## COI 0.047 0.095 0.492 0.623 0.023 0.023
## FOOD ~~
## ATMOS 0.303 0.050 6.019 0.000 0.299 0.299
## PRODQUAL 0.257 0.034 7.652 0.000 0.452 0.452
## CHOICE 0.328 0.050 6.606 0.000 0.311 0.311
## PROF 0.387 0.043 8.999 0.000 0.525 0.525
## BRAND 0.317 0.047 6.798 0.000 0.325 0.325
## FRENCH 0.469 0.047 10.016 0.000 0.588 0.588
## RI 0.123 0.023 5.283 0.000 0.258 0.258
## COI -0.044 0.063 -0.700 0.484 -0.033 -0.033
## ATMOS ~~
## PRODQUAL 0.370 0.053 7.026 0.000 0.420 0.420
## CHOICE 0.748 0.084 8.879 0.000 0.458 0.458
## PROF 0.580 0.068 8.542 0.000 0.508 0.508
## BRAND 0.785 0.080 9.748 0.000 0.520 0.520
## FRENCH 0.411 0.065 6.374 0.000 0.333 0.333
## RI 0.281 0.040 7.034 0.000 0.381 0.381
## COI 0.436 0.103 4.210 0.000 0.212 0.212
## PRODQUAL ~~
## CHOICE 0.437 0.054 8.146 0.000 0.477 0.477
## PROF 0.348 0.043 8.092 0.000 0.543 0.543
## BRAND 0.479 0.053 9.046 0.000 0.566 0.566
## FRENCH 0.211 0.038 5.621 0.000 0.305 0.305
## RI 0.112 0.022 5.128 0.000 0.270 0.270
## COI 0.060 0.058 1.036 0.300 0.052 0.052
## CHOICE ~~
## PROF 0.725 0.071 10.200 0.000 0.611 0.611
## BRAND 0.816 0.079 10.366 0.000 0.520 0.520
## FRENCH 0.296 0.061 4.829 0.000 0.231 0.231
## RI 0.216 0.037 5.829 0.000 0.282 0.282
## COI 0.068 0.100 0.678 0.498 0.032 0.032
## PROF ~~
## BRAND 0.676 0.065 10.326 0.000 0.616 0.616
## FRENCH 0.363 0.052 6.990 0.000 0.404 0.404
## RI 0.200 0.030 6.678 0.000 0.373 0.373
## COI -0.079 0.077 -1.029 0.304 -0.053 -0.053
## BRAND ~~
## FRENCH 0.388 0.061 6.333 0.000 0.327 0.327
## RI 0.188 0.034 5.501 0.000 0.265 0.265
## COI 0.111 0.094 1.190 0.234 0.056 0.056
## FRENCH ~~
## RI 0.134 0.029 4.535 0.000 0.230 0.230
## COI 0.004 0.078 0.051 0.959 0.002 0.002
## RI ~~
## COI 0.078 0.047 1.677 0.094 0.081 0.081
## .AFCOM ~~
## .SAT 0.218 0.037 5.825 0.000 0.357 0.357
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.576 0.000 4.995 3.787
## .Im4 4.999 0.057 86.999 0.000 4.999 3.713
## .Im5 5.036 0.057 87.853 0.000 5.036 3.787
## .Im10 6.100 0.037 162.781 0.000 6.100 6.936
## .Im14 6.138 0.037 165.851 0.000 6.138 7.093
## .Im20 4.672 0.064 73.228 0.000 4.672 3.125
## .Im21 5.139 0.058 87.975 0.000 5.139 3.750
## .Im22 4.280 0.065 65.485 0.000 4.280 2.802
## .Im11 5.654 0.049 115.283 0.000 5.654 4.943
## .Im12 5.666 0.049 116.116 0.000 5.666 4.985
## .Im13 5.448 0.052 105.654 0.000 5.448 4.526
## .Im1 4.792 0.057 84.287 0.000 4.792 3.600
## .Im2 4.858 0.055 88.415 0.000 4.858 3.781
## .Im16 5.135 0.052 99.179 0.000 5.135 4.269
## .Im19 5.146 0.048 107.001 0.000 5.146 4.575
## .Im17 5.025 0.053 94.560 0.000 5.025 4.043
## .Im18 4.595 0.060 76.466 0.000 4.595 3.288
## .Im6 5.827 0.051 113.792 0.000 5.827 4.858
## .Im7 5.753 0.052 110.790 0.000 5.753 4.754
## .COM_A1 4.287 0.061 70.288 0.000 4.287 3.007
## .COM_A2 3.887 0.068 57.199 0.000 3.887 2.443
## .COM_A3 3.542 0.069 51.223 0.000 3.542 2.194
## .COM_A4 3.458 0.073 47.108 0.000 3.458 2.010
## .SAT_1 5.343 0.043 124.118 0.000 5.343 5.289
## .SAT_2 5.483 0.042 129.018 0.000 5.483 5.510
## .SAT_3 5.458 0.050 109.971 0.000 5.458 4.798
## .C_REP1 4.283 0.031 136.277 0.000 4.283 5.807
## .C_REP2 4.507 0.027 167.674 0.000 4.507 7.164
## .C_REP3 4.676 0.024 195.449 0.000 4.676 8.380
## .C_CR1 2.679 0.083 32.285 0.000 2.679 1.384
## .C_CR3 3.261 0.088 37.105 0.000 3.261 1.582
## .C_CR4 2.786 0.084 33.092 0.000 2.786 1.414
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## .AFCOM 0.000 0.000 0.000
## .SAT 0.000 0.000 0.000
## RI 0.000 0.000 0.000
## COI 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.214 0.024 8.767 0.000 0.214 0.123
## .Im4 0.108 0.024 4.461 0.000 0.108 0.059
## .Im5 0.747 0.049 15.220 0.000 0.747 0.423
## .Im10 0.117 0.019 6.135 0.000 0.117 0.151
## .Im14 0.067 0.019 3.559 0.000 0.067 0.089
## .Im20 0.666 0.059 11.280 0.000 0.666 0.298
## .Im21 0.703 0.055 12.679 0.000 0.703 0.374
## .Im22 0.571 0.060 9.496 0.000 0.571 0.245
## .Im11 0.814 0.055 14.788 0.000 0.814 0.622
## .Im12 0.310 0.040 7.841 0.000 0.310 0.240
## .Im13 0.390 0.045 8.730 0.000 0.390 0.269
## .Im1 0.076 0.048 1.598 0.110 0.076 0.043
## .Im2 0.312 0.042 7.417 0.000 0.312 0.189
## .Im16 0.618 0.051 12.116 0.000 0.618 0.427
## .Im19 0.385 0.045 8.653 0.000 0.385 0.304
## .Im17 0.093 0.045 2.055 0.040 0.093 0.060
## .Im18 0.524 0.055 9.587 0.000 0.524 0.268
## .Im6 0.468 0.054 8.714 0.000 0.468 0.325
## .Im7 0.155 0.062 2.520 0.012 0.155 0.106
## .COM_A1 0.779 0.060 13.036 0.000 0.779 0.383
## .COM_A2 0.787 0.067 11.838 0.000 0.787 0.311
## .COM_A3 0.872 0.070 12.387 0.000 0.872 0.335
## .COM_A4 0.849 0.075 11.385 0.000 0.849 0.287
## .SAT_1 0.267 0.034 7.920 0.000 0.267 0.262
## .SAT_2 0.328 0.033 9.901 0.000 0.328 0.331
## .SAT_3 0.797 0.056 14.318 0.000 0.797 0.616
## .C_REP1 0.198 0.016 12.178 0.000 0.198 0.364
## .C_REP2 0.035 0.011 3.224 0.001 0.035 0.089
## .C_REP3 0.133 0.009 14.064 0.000 0.133 0.426
## .C_CR1 1.054 0.114 9.275 0.000 1.054 0.281
## .C_CR3 1.375 0.131 10.514 0.000 1.375 0.324
## .C_CR4 1.366 0.123 11.130 0.000 1.366 0.352
## DECO 1.526 0.107 14.317 0.000 1.000 1.000
## FOOD 0.657 0.049 13.302 0.000 1.000 1.000
## ATMOS 1.569 0.135 11.580 0.000 1.000 1.000
## PRODQUAL 0.494 0.067 7.362 0.000 1.000 1.000
## CHOICE 1.696 0.117 14.476 0.000 1.000 1.000
## PROF 0.829 0.086 9.605 0.000 1.000 1.000
## BRAND 1.452 0.104 14.014 0.000 1.000 1.000
## FRENCH 0.971 0.094 10.349 0.000 1.000 1.000
## .AFCOM 0.854 0.086 9.878 0.000 0.681 0.681
## .SAT 0.436 0.050 8.755 0.000 0.579 0.579
## RI 0.346 0.032 10.668 0.000 1.000 1.000
## COI 2.693 0.238 11.334 0.000 1.000 1.000
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN NaN NaN NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_3 NaN NaN NaN NaN NaN NaN NaN NaN NaN 0.384 NaN NaN
## C_REP1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO 1
## FOOD NaN 1
## ATMOS NaN NaN 1
## PRODQUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## PROF NaN NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN NaN 1
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FOOD 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## ATMOS 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PRODQUAL 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## CHOICE 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PROF 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## BRAND 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## AFCOM 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## SAT 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## RI 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## COI 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH AFCOM SAT RI COI
## DECO 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FOOD 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## ATMOS 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PRODQUAL 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## CHOICE 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PROF 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## BRAND 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FRENCH 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## AFCOM 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## SAT 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## RI 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## COI 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO 1.000
## FOOD 0.416 1.000
## ATMOS 0.472 0.299 1.000
## PRODQUAL 0.470 0.452 0.420 1.000
## CHOICE 0.441 0.311 0.458 0.477 1.000
## PROF 0.667 0.525 0.508 0.543 0.611 1.000
## BRAND 0.516 0.325 0.520 0.566 0.520 0.616 1.000
## FRENCH 0.338 0.588 0.333 0.305 0.231 0.404 0.327 1.000
## AFCOM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.681
## SAT 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.357 0.579
## RI 0.249 0.258 0.381 0.270 0.282 0.373 0.265 0.230 0.000 0.000
## COI 0.023 -0.033 0.212 0.052 0.032 -0.053 0.056 0.002 0.000 0.000
## RI COI
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI 1.000
## COI 0.081 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN .
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN .
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI COI
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI .
## COI NaN .
arrange(modificationindices(SEM_fit),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 AFCOM =~ C_REP1 61.877 0.158 0.177 0.240 0.240
## 2 ATMOS ~~ AFCOM 49.054 -0.587 -0.507 -0.507 -0.507
## 3 ATMOS ~ AFCOM 35.588 -0.540 -0.483 -0.483 -0.483
## 4 AFCOM ~~ RI 32.373 0.134 0.247 0.247 0.247
## 5 COM_A1 ~~ COM_A2 31.301 0.288 0.288 0.368 0.368
## 6 AFCOM ~~ COI 31.255 0.406 0.268 0.268 0.268
## 7 ATMOS =~ C_REP1 26.283 0.102 0.127 0.173 0.173
## 8 Im16 ~~ Im19 25.773 0.371 0.371 0.761 0.761
## 9 PROF ~~ SAT 25.773 -0.222 -0.368 -0.368 -0.368
## 10 BRAND =~ Im13 23.807 0.219 0.264 0.219 0.219
## 11 C_REP2 ~~ C_REP3 23.244 0.096 0.096 1.407 1.407
## 12 SAT ~~ RI 22.140 0.089 0.229 0.229 0.229
## 13 Im11 ~~ Im13 21.621 -0.192 -0.192 -0.341 -0.341
## 14 SAT =~ C_REP1 18.223 0.115 0.099 0.135 0.135
## 15 RI =~ SAT_2 17.895 0.232 0.137 0.137 0.137
## 16 BRAND =~ Im12 17.152 -0.178 -0.214 -0.189 -0.189
## 17 CHOICE =~ Im20 16.326 -0.160 -0.208 -0.139 -0.139
## 18 RI =~ Im22 15.906 -0.338 -0.199 -0.130 -0.130
## 19 RI =~ COM_A1 15.392 0.299 0.176 0.123 0.123
## 20 PROF ~ SAT 14.568 -0.337 -0.322 -0.322 -0.322
## 21 CHOICE =~ Im13 14.137 0.134 0.175 0.145 0.145
## 22 Im11 ~~ Im12 13.137 0.144 0.144 0.286 0.286
## 23 COM_A3 ~~ C_REP1 13.055 0.078 0.078 0.188 0.188
## 24 FOOD =~ Im11 12.685 0.215 0.174 0.152 0.152
## 25 AFCOM =~ Im11 11.893 0.138 0.154 0.135 0.135
## 26 CHOICE =~ C_REP1 11.775 0.059 0.077 0.104 0.104
## 27 SAT ~ FRENCH 11.592 0.143 0.163 0.163 0.163
## 28 PRODQUAL =~ C_CR4 11.365 0.307 0.216 0.109 0.109
## 29 PROF =~ COM_A3 11.354 0.198 0.180 0.112 0.112
## 30 Im21 ~~ C_REP3 11.319 0.052 0.052 0.171 0.171
## 31 ATMOS =~ Im12 11.112 -0.116 -0.146 -0.128 -0.128
## 32 AFCOM =~ Im20 10.705 -0.168 -0.188 -0.126 -0.126
## 33 FRENCH =~ C_REP1 10.658 0.075 0.074 0.100 0.100
## 34 CHOICE =~ Im12 10.534 -0.111 -0.144 -0.127 -0.127
## 35 Im21 ~~ Im22 10.334 -0.190 -0.190 -0.299 -0.299
## 36 Im13 ~~ Im1 10.251 0.066 0.066 0.382 0.382
## 37 PRODQUAL ~~ AFCOM 9.881 -0.142 -0.219 -0.219 -0.219
## 38 DECO =~ C_REP1 9.764 0.056 0.069 0.094 0.094
## 39 AFCOM ~ CHOICE 9.453 0.130 0.151 0.151 0.151
## 40 SAT =~ COM_A2 9.449 -0.194 -0.168 -0.106 -0.106
## 41 Im13 ~~ Im17 9.292 0.068 0.068 0.358 0.358
## 42 SAT =~ COM_A3 9.262 0.199 0.173 0.107 0.107
## 43 AFCOM ~ SAT 9.120 0.359 0.278 0.278 0.278
## 44 Im4 ~~ Im17 9.042 -0.045 -0.045 -0.453 -0.453
## 45 Im1 ~~ SAT_2 9.041 -0.055 -0.055 -0.346 -0.346
## 46 PRODQUAL ~ AFCOM 8.849 -0.148 -0.235 -0.235 -0.235
## 47 SAT ~ AFCOM 8.555 0.220 0.284 0.284 0.284
## 48 Im20 ~~ Im22 8.506 0.205 0.205 0.333 0.333
## 49 Im10 ~~ Im16 8.198 0.046 0.046 0.173 0.173
## 50 SAT =~ Im12 8.068 -0.129 -0.112 -0.099 -0.099
## 51 ATMOS =~ Im11 7.837 0.111 0.138 0.121 0.121
## 52 AFCOM =~ Im12 7.657 -0.091 -0.102 -0.090 -0.090
## 53 Im14 ~~ Im16 7.416 -0.043 -0.043 -0.212 -0.212
## 54 Im20 ~~ Im21 7.388 0.150 0.150 0.219 0.219
## 55 PRODQUAL =~ C_CR1 7.333 -0.237 -0.166 -0.086 -0.086
## 56 FRENCH =~ Im22 7.319 0.137 0.135 0.088 0.088
## 57 COI =~ C_REP1 7.224 0.036 0.060 0.081 0.081
## 58 ATMOS =~ C_CR4 7.213 0.140 0.176 0.089 0.089
## 59 Im10 ~~ COM_A2 7.207 0.049 0.049 0.162 0.162
## 60 DECO =~ COM_A3 7.153 0.107 0.132 0.082 0.082
## 61 BRAND =~ Im20 7.150 -0.123 -0.148 -0.099 -0.099
## 62 FOOD =~ C_REP1 7.149 0.074 0.060 0.081 0.081
## 63 CHOICE =~ C_REP3 7.114 -0.037 -0.048 -0.086 -0.086
## 64 SAT =~ C_CR4 7.053 0.194 0.169 0.086 0.086
## 65 COM_A1 ~~ COM_A4 7.039 -0.148 -0.148 -0.183 -0.183
## 66 FRENCH =~ C_REP2 7.027 -0.050 -0.050 -0.079 -0.079
## 67 ATMOS =~ C_REP3 6.995 -0.042 -0.053 -0.094 -0.094
## 68 AFCOM ~ PROF 6.907 0.199 0.162 0.162 0.162
## 69 BRAND =~ Im22 6.898 0.122 0.148 0.097 0.097
## 70 SAT ~~ COI 6.822 -0.152 -0.140 -0.140 -0.140
## 71 Im19 ~~ C_REP1 6.618 -0.040 -0.040 -0.145 -0.145
## 72 RI =~ Im16 6.453 -0.207 -0.122 -0.101 -0.101
## 73 Im10 ~~ Im6 6.414 -0.036 -0.036 -0.152 -0.152
## 74 FRENCH =~ Im16 6.315 -0.127 -0.126 -0.104 -0.104
## 75 CHOICE =~ Im5 6.298 0.086 0.112 0.085 0.085
## 76 BRAND =~ Im4 6.287 -0.067 -0.081 -0.060 -0.060
## 77 PROF =~ Im12 6.238 -0.152 -0.138 -0.122 -0.122
## 78 PRODQUAL =~ Im5 6.228 0.173 0.121 0.091 0.091
## 79 BRAND =~ C_CR4 6.197 0.127 0.153 0.078 0.078
## 80 PROF =~ C_REP1 6.135 0.069 0.062 0.085 0.085
## 81 Im22 ~~ Im1 6.117 0.062 0.062 0.296 0.296
## 82 ATMOS =~ Im5 6.069 0.095 0.119 0.089 0.089
## 83 C_REP1 ~~ C_REP2 6.068 -0.076 -0.076 -0.909 -0.909
## 84 SAT_2 ~~ SAT_3 6.011 -0.090 -0.090 -0.177 -0.177
## 85 DECO =~ C_CR4 5.821 0.119 0.147 0.075 0.075
## 86 BRAND =~ Im5 5.807 0.096 0.115 0.087 0.087
## 87 FOOD =~ Im6 5.787 -0.269 -0.218 -0.182 -0.182
## 88 BRAND =~ COM_A3 5.704 0.099 0.120 0.074 0.074
## 89 PROF =~ C_CR4 5.642 0.168 0.153 0.078 0.078
## 90 Im13 ~~ Im16 5.612 -0.070 -0.070 -0.144 -0.144
## 91 DECO =~ Im18 5.593 0.101 0.125 0.089 0.089
## 92 DECO =~ Im17 5.593 -0.102 -0.126 -0.101 -0.101
## 93 SAT_1 ~~ SAT_3 5.570 0.092 0.092 0.200 0.200
## 94 COM_A3 ~~ COM_A4 5.532 0.152 0.152 0.176 0.176
## 95 Im3 ~~ Im1 5.490 -0.034 -0.034 -0.265 -0.265
## 96 Im10 ~~ Im7 5.466 0.034 0.034 0.252 0.252
## 97 COM_A1 ~~ C_REP2 5.455 0.034 0.034 0.207 0.207
## 98 Im22 ~~ Im12 5.408 -0.068 -0.068 -0.163 -0.163
## 99 Im11 ~~ Im6 5.400 -0.072 -0.072 -0.116 -0.116
## 100 AFCOM =~ C_CR4 5.370 0.129 0.144 0.073 0.073
## 101 Im22 ~~ C_REP2 5.355 -0.033 -0.033 -0.234 -0.234
## 102 Im16 ~~ SAT_1 5.322 -0.061 -0.061 -0.150 -0.150
## 103 ATMOS =~ C_REP2 5.286 -0.039 -0.049 -0.077 -0.077
## 104 FOOD =~ COM_A3 5.281 0.140 0.113 0.070 0.070
## 105 Im1 ~~ SAT_1 5.167 0.041 0.041 0.287 0.287
## 106 DECO =~ Im20 5.076 -0.095 -0.117 -0.079 -0.079
## 107 DECO =~ C_REP3 5.036 -0.032 -0.040 -0.072 -0.072
## 108 FOOD =~ Im13 5.010 -0.125 -0.102 -0.084 -0.084
## 109 Im5 ~~ Im6 5.010 -0.066 -0.066 -0.112 -0.112
## 110 DECO =~ C_CR1 5.008 -0.106 -0.131 -0.068 -0.068
## 111 DECO =~ Im7 4.885 -0.084 -0.104 -0.086 -0.086
## 112 PROF =~ COM_A2 4.882 -0.125 -0.114 -0.071 -0.071
## 113 CHOICE ~~ AFCOM 4.865 0.101 0.084 0.084 0.084
## 114 C_REP1 ~~ C_REP3 4.856 -0.036 -0.036 -0.225 -0.225
## 115 Im4 ~~ C_CR1 4.822 -0.064 -0.064 -0.191 -0.191
## 116 Im4 ~~ Im18 4.818 0.040 0.040 0.168 0.168
## 117 Im10 ~~ Im13 4.805 -0.031 -0.031 -0.145 -0.145
## 118 FOOD =~ C_REP2 4.798 -0.051 -0.041 -0.065 -0.065
## 119 Im13 ~~ Im2 4.787 -0.045 -0.045 -0.129 -0.129
## 120 Im3 ~~ Im22 4.764 0.049 0.049 0.139 0.139
## 121 FRENCH =~ Im20 4.724 -0.109 -0.107 -0.072 -0.072
## 122 FOOD =~ Im5 4.677 0.120 0.097 0.073 0.073
## 123 FOOD =~ Im7 4.663 0.284 0.230 0.190 0.190
## 124 Im22 ~~ C_REP3 4.654 -0.034 -0.034 -0.123 -0.123
## 125 Im20 ~~ Im17 4.627 -0.058 -0.058 -0.233 -0.233
## 126 PROF =~ SAT_2 4.584 0.130 0.118 0.119 0.119
## 127 Im22 ~~ SAT_1 4.558 0.058 0.058 0.148 0.148
## 128 PROF =~ C_REP3 4.558 -0.048 -0.043 -0.078 -0.078
## 129 Im4 ~~ COM_A3 4.540 0.051 0.051 0.168 0.168
## 130 BRAND =~ C_CR1 4.516 -0.104 -0.126 -0.065 -0.065
## 131 CHOICE ~ AFCOM 4.498 0.114 0.098 0.098 0.098
## 132 Im11 ~~ C_REP1 4.467 0.041 0.041 0.102 0.102
## 133 COM_A1 ~~ SAT_1 4.359 -0.059 -0.059 -0.128 -0.128
## 134 COI =~ COM_A4 4.335 0.063 0.104 0.060 0.060
## 135 Im3 ~~ Im4 4.333 0.148 0.148 0.977 0.977
## 136 RI =~ Im12 4.281 -0.133 -0.078 -0.069 -0.069
## 137 Im3 ~~ Im5 4.266 -0.068 -0.068 -0.169 -0.169
## 138 FRENCH ~~ SAT 4.214 0.060 0.093 0.093 0.093
## 139 COI =~ SAT_1 4.213 -0.039 -0.064 -0.063 -0.063
## 140 BRAND =~ Im7 4.204 -0.079 -0.096 -0.079 -0.079
## 141 AFCOM =~ Im5 4.180 0.079 0.088 0.066 0.066
## 142 DECO =~ Im6 4.175 0.067 0.083 0.069 0.069
## 143 RI =~ Im21 4.151 0.163 0.096 0.070 0.070
## 144 ATMOS =~ Im4 4.122 -0.052 -0.065 -0.048 -0.048
## 145 Im14 ~~ COM_A2 4.095 -0.036 -0.036 -0.156 -0.156
## 146 PRODQUAL =~ Im2 4.068 -0.124 -0.087 -0.068 -0.068
## 147 DECO =~ COM_A2 4.009 -0.077 -0.095 -0.059 -0.059
## 148 Im20 ~~ Im6 3.960 -0.062 -0.062 -0.111 -0.111
## 149 CHOICE =~ COM_A3 3.948 0.074 0.097 0.060 0.060
## 150 PROF =~ Im13 3.914 0.126 0.114 0.095 0.095
## 151 SAT =~ C_CR1 3.891 -0.138 -0.120 -0.062 -0.062
## 152 PROF =~ Im20 3.844 -0.126 -0.115 -0.077 -0.077
## 153 BRAND =~ C_REP3 3.843 -0.029 -0.036 -0.064 -0.064
## 154 Im16 ~~ C_REP3 3.839 -0.029 -0.029 -0.102 -0.102
## 155 BRAND =~ Im6 3.805 0.065 0.079 0.066 0.066
## 156 PRODQUAL =~ Im1 3.759 0.134 0.094 0.071 0.071
## 157 Im7 ~~ C_REP2 3.754 -0.022 -0.022 -0.298 -0.298
## 158 DECO =~ Im22 3.749 0.083 0.102 0.067 0.067
## 159 COM_A4 ~~ C_CR4 3.747 0.121 0.121 0.112 0.112
## 160 FOOD =~ C_CR4 3.740 0.147 0.119 0.060 0.060
## 161 SAT ~ ATMOS 3.739 0.072 0.104 0.104 0.104
## 162 SAT_3 ~~ C_CR3 3.717 -0.111 -0.111 -0.106 -0.106
## 163 COI =~ Im19 3.711 0.050 0.083 0.073 0.073
## 164 COM_A2 ~~ SAT_2 3.687 -0.057 -0.057 -0.113 -0.113
## 165 Im20 ~~ COM_A4 3.684 0.085 0.085 0.113 0.113
## 166 Im20 ~~ Im13 3.683 0.061 0.061 0.120 0.120
## 167 Im4 ~~ Im6 3.674 0.033 0.033 0.148 0.148
## 168 Im11 ~~ Im1 3.661 -0.047 -0.047 -0.190 -0.190
## 169 Im22 ~~ SAT_2 3.643 -0.053 -0.053 -0.121 -0.121
## 170 RI =~ Im5 3.628 0.136 0.080 0.060 0.060
## 171 COM_A1 ~~ COM_A3 3.553 -0.099 -0.099 -0.120 -0.120
## 172 COM_A2 ~~ COM_A3 3.545 -0.111 -0.111 -0.134 -0.134
## 173 SAT_1 ~~ C_CR1 3.534 -0.069 -0.069 -0.130 -0.130
## 174 Im3 ~~ COM_A4 3.528 0.048 0.048 0.112 0.112
## 175 Im22 ~~ Im11 3.500 0.071 0.071 0.105 0.105
## 176 PROF =~ C_CR1 3.432 -0.126 -0.115 -0.059 -0.059
## 177 Im2 ~~ Im17 3.429 0.032 0.032 0.188 0.188
## 178 ATMOS =~ COM_A4 3.391 0.094 0.118 0.069 0.069
## 179 Im3 ~~ Im17 3.378 0.028 0.028 0.201 0.201
## 180 Im13 ~~ C_REP2 3.372 0.022 0.022 0.185 0.185
## 181 Im22 ~~ C_REP1 3.355 0.035 0.035 0.105 0.105
## 182 PROF =~ Im2 3.355 0.161 0.147 0.114 0.114
## 183 PROF =~ Im1 3.354 -0.181 -0.165 -0.124 -0.124
## 184 C_REP2 ~~ C_CR4 3.348 -0.037 -0.037 -0.171 -0.171
## 185 FRENCH ~ SAT 3.327 0.124 0.109 0.109 0.109
## 186 Im13 ~~ C_REP1 3.251 -0.029 -0.029 -0.103 -0.103
## 187 Im20 ~~ SAT_2 3.249 0.050 0.050 0.108 0.108
## 188 Im14 ~~ Im6 3.218 0.025 0.025 0.142 0.142
## 189 COI =~ C_REP2 3.212 -0.020 -0.033 -0.052 -0.052
## 190 Im22 ~~ COM_A1 3.204 -0.071 -0.071 -0.106 -0.106
## 191 AFCOM =~ C_REP3 3.175 -0.029 -0.033 -0.058 -0.058
## 192 COI =~ Im11 3.174 0.048 0.078 0.069 0.069
## 193 PROF =~ SAT_1 3.159 -0.113 -0.103 -0.102 -0.102
## 194 Im1 ~~ C_REP3 3.154 -0.018 -0.018 -0.179 -0.179
## 195 Im11 ~~ Im17 3.129 -0.047 -0.047 -0.169 -0.169
## 196 COM_A2 ~~ C_CR1 3.120 0.099 0.099 0.108 0.108
## 197 Im20 ~~ COM_A2 3.119 -0.074 -0.074 -0.102 -0.102
## 198 Im18 ~~ Im6 3.098 0.046 0.046 0.092 0.092
## 199 Im17 ~~ C_REP1 3.076 -0.023 -0.023 -0.172 -0.172
## 200 Im5 ~~ C_REP1 3.034 0.032 0.032 0.084 0.084
## 201 FRENCH =~ Im11 3.032 0.081 0.080 0.070 0.070
## 202 PRODQUAL =~ Im16 3.000 -0.148 -0.104 -0.087 -0.087
## 203 Im14 ~~ SAT_2 2.981 0.021 0.021 0.139 0.139
## 204 PRODQUAL =~ C_REP3 2.970 -0.046 -0.033 -0.059 -0.059
## 205 Im18 ~~ COM_A1 2.961 -0.057 -0.057 -0.090 -0.090
## 206 Im3 ~~ Im2 2.955 0.025 0.025 0.097 0.097
## 207 BRAND =~ C_REP1 2.929 0.032 0.038 0.052 0.052
## 208 COM_A1 ~~ C_CR3 2.928 0.099 0.099 0.096 0.096
## 209 Im13 ~~ COM_A2 2.909 -0.058 -0.058 -0.104 -0.104
## 210 Im14 ~~ Im7 2.900 -0.025 -0.025 -0.243 -0.243
## 211 COM_A4 ~~ SAT_1 2.891 0.053 0.053 0.111 0.111
## 212 FRENCH =~ C_CR4 2.880 0.108 0.106 0.054 0.054
## 213 Im5 ~~ Im1 2.857 0.040 0.040 0.168 0.168
## 214 FRENCH =~ COM_A3 2.841 0.090 0.089 0.055 0.055
## 215 ATMOS =~ COM_A1 2.817 -0.076 -0.095 -0.067 -0.067
## 216 Im10 ~~ Im11 2.794 0.028 0.028 0.092 0.092
## 217 Im22 ~~ Im2 2.792 -0.042 -0.042 -0.099 -0.099
## 218 SAT =~ Im19 2.751 -0.121 -0.105 -0.093 -0.093
## 219 Im10 ~~ C_CR1 2.731 0.038 0.038 0.109 0.109
## 220 Im14 ~~ C_CR1 2.727 -0.037 -0.037 -0.140 -0.140
## 221 SAT_2 ~~ C_REP1 2.724 0.023 0.023 0.090 0.090
## 222 Im5 ~~ Im14 2.721 0.026 0.026 0.117 0.117
## 223 Im2 ~~ C_CR1 2.710 0.056 0.056 0.098 0.098
## 224 RI =~ Im11 2.694 0.124 0.073 0.064 0.064
## 225 Im5 ~~ Im7 2.692 0.047 0.047 0.137 0.137
## 226 COM_A1 ~~ SAT_3 2.689 0.066 0.066 0.084 0.084
## 227 SAT =~ Im5 2.676 0.086 0.074 0.056 0.056
## 228 Im21 ~~ C_CR3 2.672 -0.091 -0.091 -0.092 -0.092
## 229 Im2 ~~ SAT_2 2.671 0.030 0.030 0.093 0.093
## 230 Im1 ~~ Im17 2.669 -0.029 -0.029 -0.347 -0.347
## 231 Im12 ~~ Im7 2.643 0.038 0.038 0.172 0.172
## 232 SAT =~ Im20 2.596 -0.092 -0.080 -0.053 -0.053
## 233 Im19 ~~ SAT_1 2.588 -0.038 -0.038 -0.117 -0.117
## 234 Im2 ~~ Im16 2.587 0.038 0.038 0.087 0.087
## 235 COM_A2 ~~ SAT_1 2.580 -0.047 -0.047 -0.103 -0.103
## 236 Im20 ~~ COM_A1 2.563 -0.064 -0.064 -0.089 -0.089
## 237 CHOICE =~ Im22 2.551 0.064 0.083 0.054 0.054
## 238 ATMOS =~ C_CR1 2.545 -0.080 -0.100 -0.052 -0.052
## 239 ATMOS =~ Im13 2.531 0.058 0.073 0.061 0.061
## 240 C_REP3 ~~ C_CR3 2.505 -0.037 -0.037 -0.086 -0.086
## 241 Im14 ~~ C_REP3 2.490 0.011 0.011 0.114 0.114
## 242 AFCOM =~ SAT_2 2.425 0.053 0.060 0.060 0.060
## 243 Im2 ~~ C_REP1 2.403 0.020 0.020 0.079 0.079
## 244 Im4 ~~ Im11 2.402 -0.033 -0.033 -0.112 -0.112
## 245 Im3 ~~ C_CR1 2.396 0.047 0.047 0.099 0.099
## 246 Im4 ~~ Im22 2.381 -0.033 -0.033 -0.134 -0.134
## 247 COM_A4 ~~ SAT_3 2.375 -0.069 -0.069 -0.083 -0.083
## 248 CHOICE =~ Im14 2.365 0.026 0.034 0.039 0.039
## 249 CHOICE =~ Im10 2.364 -0.025 -0.033 -0.038 -0.038
## 250 Im5 ~~ COM_A2 2.363 0.061 0.061 0.079 0.079
## 251 FOOD =~ C_CR1 2.363 -0.112 -0.091 -0.047 -0.047
## 252 Im22 ~~ SAT_3 2.338 -0.060 -0.060 -0.088 -0.088
## 253 Im11 ~~ C_REP2 2.334 -0.022 -0.022 -0.128 -0.128
## 254 SAT =~ Im11 2.319 0.084 0.073 0.064 0.064
## 255 FOOD =~ SAT_2 2.311 0.063 0.051 0.052 0.052
## 256 Im20 ~~ Im1 2.293 -0.038 -0.038 -0.169 -0.169
## 257 COM_A4 ~~ C_REP1 2.283 0.033 0.033 0.081 0.081
## 258 PRODQUAL =~ SAT_2 2.262 0.078 0.055 0.055 0.055
## 259 COM_A3 ~~ C_REP2 2.256 -0.024 -0.024 -0.136 -0.136
## 260 COM_A2 ~~ COM_A4 2.244 -0.096 -0.096 -0.118 -0.118
## 261 SAT =~ Im16 2.223 -0.113 -0.098 -0.081 -0.081
## 262 FRENCH =~ Im1 2.216 -0.051 -0.050 -0.038 -0.038
## 263 FOOD =~ Im16 2.214 -0.100 -0.081 -0.067 -0.067
## 264 Im21 ~~ Im18 2.214 -0.047 -0.047 -0.078 -0.078
## 265 Im13 ~~ COM_A3 2.212 -0.052 -0.052 -0.090 -0.090
## 266 SAT =~ Im13 2.196 0.072 0.062 0.052 0.052
## 267 Im2 ~~ C_REP2 2.177 -0.014 -0.014 -0.131 -0.131
## 268 Im22 ~~ Im7 2.176 0.044 0.044 0.149 0.149
## 269 Im19 ~~ COM_A1 2.173 0.047 0.047 0.086 0.086
## 270 AFCOM =~ Im2 2.170 0.041 0.045 0.035 0.035
## 271 COM_A3 ~~ C_REP3 2.156 -0.026 -0.026 -0.076 -0.076
## 272 DECO =~ Im12 2.149 -0.052 -0.065 -0.057 -0.057
## 273 Im5 ~~ Im16 2.143 -0.051 -0.051 -0.074 -0.074
## 274 Im13 ~~ SAT_2 2.137 0.033 0.033 0.092 0.092
## 275 FRENCH =~ SAT_1 2.131 0.048 0.048 0.047 0.047
## 276 Im3 ~~ Im20 2.127 -0.033 -0.033 -0.087 -0.087
## 277 COI =~ Im2 2.123 0.025 0.042 0.032 0.032
## 278 Im4 ~~ Im1 2.121 0.020 0.020 0.226 0.226
## 279 COI =~ Im13 2.103 -0.034 -0.056 -0.046 -0.046
## 280 COI =~ COM_A2 2.066 0.041 0.068 0.043 0.043
## 281 Im3 ~~ COM_A3 2.063 -0.036 -0.036 -0.084 -0.084
## 282 BRAND =~ SAT_2 2.060 0.043 0.052 0.052 0.052
## 283 PRODQUAL =~ Im6 2.054 -0.086 -0.060 -0.050 -0.050
## 284 PRODQUAL =~ Im7 2.054 0.100 0.070 0.058 0.058
## 285 Im22 ~~ Im19 2.047 -0.045 -0.045 -0.095 -0.095
## 286 Im10 ~~ Im17 2.044 -0.017 -0.017 -0.162 -0.162
## 287 Im16 ~~ C_CR4 2.028 -0.074 -0.074 -0.080 -0.080
## 288 Im22 ~~ Im18 2.023 0.046 0.046 0.084 0.084
## 289 FRENCH =~ COM_A2 2.019 -0.073 -0.072 -0.045 -0.045
## 290 Im3 ~~ Im12 2.015 -0.024 -0.024 -0.094 -0.094
## 291 Im12 ~~ Im16 2.003 0.039 0.039 0.090 0.090
## 292 Im2 ~~ SAT_1 1.991 -0.025 -0.025 -0.087 -0.087
## 293 Im12 ~~ SAT_3 1.984 0.042 0.042 0.085 0.085
## 294 Im18 ~~ C_REP1 1.983 0.023 0.023 0.071 0.071
## 295 Im19 ~~ C_REP2 1.960 0.017 0.017 0.143 0.143
## 296 Im21 ~~ C_CR4 1.960 0.076 0.076 0.077 0.077
## 297 Im14 ~~ Im17 1.948 0.016 0.016 0.206 0.206
## 298 Im2 ~~ COM_A3 1.923 0.039 0.039 0.075 0.075
## 299 SAT =~ Im18 1.917 -0.073 -0.064 -0.046 -0.046
## 300 Im14 ~~ COM_A3 1.909 0.026 0.026 0.106 0.106
## 301 Im14 ~~ Im2 1.900 0.015 0.015 0.103 0.103
## 302 FOOD =~ Im1 1.888 -0.060 -0.049 -0.037 -0.037
## 303 Im12 ~~ SAT_1 1.877 -0.028 -0.028 -0.098 -0.098
## 304 C_CR1 ~~ C_CR3 1.851 0.543 0.543 0.451 0.451
## 305 Im10 ~~ COM_A4 1.834 -0.026 -0.026 -0.083 -0.083
## 306 Im7 ~~ COM_A1 1.820 -0.041 -0.041 -0.119 -0.119
## 307 Im11 ~~ Im7 1.810 0.040 0.040 0.112 0.112
## 308 Im11 ~~ COM_A3 1.799 0.058 0.058 0.068 0.068
## 309 COM_A3 ~~ SAT_2 1.794 0.042 0.042 0.078 0.078
## 310 SAT =~ Im2 1.787 0.065 0.056 0.044 0.044
## 311 BRAND =~ Im3 1.782 0.035 0.042 0.032 0.032
## 312 Im20 ~~ SAT_1 1.779 -0.036 -0.036 -0.086 -0.086
## 313 COM_A2 ~~ SAT_3 1.771 0.056 0.056 0.071 0.071
## 314 COM_A1 ~~ C_REP3 1.769 0.022 0.022 0.067 0.067
## 315 CHOICE =~ SAT_2 1.768 -0.041 -0.054 -0.054 -0.054
## 316 CHOICE =~ C_CR4 1.742 0.062 0.080 0.041 0.041
## 317 ATMOS =~ SAT_2 1.740 0.037 0.047 0.047 0.047
## 318 PROF =~ Im4 1.737 -0.065 -0.059 -0.044 -0.044
## 319 Im10 ~~ SAT_2 1.735 -0.016 -0.016 -0.083 -0.083
## 320 FRENCH =~ Im5 1.729 0.059 0.058 0.043 0.043
## 321 Im19 ~~ Im17 1.718 0.030 0.030 0.158 0.158
## 322 FRENCH =~ C_CR1 1.715 -0.080 -0.079 -0.041 -0.041
## 323 Im20 ~~ COM_A3 1.713 -0.057 -0.057 -0.075 -0.075
## 324 Im7 ~~ COM_A2 1.692 -0.042 -0.042 -0.119 -0.119
## 325 COI =~ Im1 1.689 -0.025 -0.042 -0.031 -0.031
## 326 Im12 ~~ Im6 1.663 -0.030 -0.030 -0.080 -0.080
## 327 RI =~ Im14 1.662 0.047 0.028 0.032 0.032
## 328 RI =~ Im10 1.662 -0.046 -0.027 -0.031 -0.031
## 329 Im13 ~~ COM_A4 1.659 0.046 0.046 0.080 0.080
## 330 RI =~ Im7 1.647 -0.094 -0.055 -0.046 -0.046
## 331 Im11 ~~ Im2 1.627 0.032 0.032 0.063 0.063
## 332 COI =~ Im22 1.622 -0.037 -0.061 -0.040 -0.040
## 333 Im3 ~~ Im14 1.617 -0.012 -0.012 -0.103 -0.103
## 334 C_REP1 ~~ C_CR3 1.612 0.036 0.036 0.069 0.069
## 335 Im5 ~~ SAT_2 1.610 0.034 0.034 0.068 0.068
## 336 PRODQUAL =~ Im4 1.608 -0.058 -0.041 -0.030 -0.030
## 337 RI =~ Im19 1.585 -0.099 -0.058 -0.052 -0.052
## 338 Im12 ~~ C_CR4 1.580 0.053 0.053 0.081 0.081
## 339 COI =~ Im4 1.558 -0.020 -0.032 -0.024 -0.024
## 340 SAT =~ Im17 1.554 0.057 0.049 0.040 0.040
## 341 Im7 ~~ SAT_3 1.540 0.038 0.038 0.107 0.107
## 342 Im12 ~~ Im17 1.539 -0.026 -0.026 -0.154 -0.154
## 343 Im17 ~~ COM_A1 1.518 0.033 0.033 0.124 0.124
## 344 FRENCH =~ Im2 1.509 0.038 0.037 0.029 0.029
## 345 Im1 ~~ COM_A4 1.504 -0.034 -0.034 -0.135 -0.135
## 346 Im10 ~~ Im18 1.499 0.018 0.018 0.071 0.071
## 347 Im4 ~~ Im2 1.495 -0.017 -0.017 -0.094 -0.094
## 348 RI =~ Im13 1.495 0.082 0.048 0.040 0.040
## 349 CHOICE =~ Im21 1.486 0.046 0.060 0.043 0.043
## 350 Im2 ~~ Im18 1.484 -0.026 -0.026 -0.063 -0.063
## 351 CHOICE ~ SAT 1.479 0.210 0.140 0.140 0.140
## 352 C_REP3 ~~ C_CR4 1.479 0.027 0.027 0.064 0.064
## 353 Im11 ~~ SAT_1 1.457 0.033 0.033 0.070 0.070
## 354 PROF =~ Im5 1.424 0.081 0.074 0.055 0.055
## 355 DECO =~ Im13 1.423 0.045 0.055 0.046 0.046
## 356 Im12 ~~ Im13 1.421 0.088 0.088 0.252 0.252
## 357 Im18 ~~ COM_A2 1.416 0.041 0.041 0.064 0.064
## 358 COM_A1 ~~ SAT_2 1.415 0.034 0.034 0.067 0.067
## 359 FOOD =~ Im2 1.413 0.046 0.038 0.029 0.029
## 360 Im12 ~~ C_REP1 1.409 -0.018 -0.018 -0.071 -0.071
## 361 AFCOM ~ DECO 1.398 0.054 0.059 0.059 0.059
## 362 DECO ~~ SAT 1.396 -0.146 -0.179 -0.179 -0.179
## 363 Im14 ~~ Im18 1.395 -0.016 -0.016 -0.088 -0.088
## 364 Im21 ~~ SAT_3 1.392 0.045 0.045 0.061 0.061
## 365 SAT =~ COM_A1 1.385 0.070 0.061 0.043 0.043
## 366 Im1 ~~ COM_A1 1.385 0.030 0.030 0.123 0.123
## 367 Im18 ~~ Im7 1.381 -0.029 -0.029 -0.103 -0.103
## 368 COM_A3 ~~ C_CR3 1.376 0.074 0.074 0.068 0.068
## 369 SAT_2 ~~ C_CR3 1.376 0.048 0.048 0.071 0.071
## 370 Im14 ~~ C_CR4 1.375 0.028 0.028 0.092 0.092
## 371 Im10 ~~ Im12 1.375 0.015 0.015 0.081 0.081
## 372 SAT =~ Im4 1.372 -0.039 -0.034 -0.025 -0.025
## 373 AFCOM =~ Im16 1.367 -0.047 -0.053 -0.044 -0.044
## 374 Im3 ~~ Im18 1.357 -0.022 -0.022 -0.066 -0.066
## 375 Im19 ~~ Im18 1.354 -0.031 -0.031 -0.068 -0.068
## 376 Im18 ~~ C_REP3 1.351 -0.015 -0.015 -0.058 -0.058
## 377 ATMOS =~ Im17 1.348 -0.052 -0.065 -0.053 -0.053
## 378 ATMOS =~ Im18 1.348 0.052 0.065 0.046 0.046
## 379 Im4 ~~ Im12 1.347 0.019 0.019 0.105 0.105
## 380 CHOICE =~ COM_A1 1.346 0.040 0.052 0.036 0.036
## 381 Im5 ~~ Im19 1.341 -0.034 -0.034 -0.064 -0.064
## 382 Im13 ~~ SAT_3 1.338 -0.037 -0.037 -0.066 -0.066
## 383 Im3 ~~ Im11 1.307 0.026 0.026 0.061 0.061
## 384 SAT_1 ~~ C_CR4 1.304 0.044 0.044 0.073 0.073
## 385 ATMOS =~ COM_A2 1.298 -0.055 -0.069 -0.043 -0.043
## 386 Im20 ~~ C_REP2 1.295 0.016 0.016 0.108 0.108
## 387 BRAND =~ Im16 1.284 -0.059 -0.071 -0.059 -0.059
## 388 SAT_1 ~~ C_REP3 1.284 0.013 0.013 0.067 0.067
## 389 Im6 ~~ Im7 1.281 0.435 0.435 1.612 1.612
## 390 FRENCH ~~ AFCOM 1.280 -0.077 -0.085 -0.085 -0.085
## 391 RI =~ COM_A3 1.276 0.094 0.055 0.034 0.034
## 392 PRODQUAL =~ Im17 1.271 0.103 0.072 0.058 0.058
## 393 PRODQUAL =~ Im18 1.271 -0.102 -0.072 -0.051 -0.051
## 394 Im14 ~~ Im21 1.262 0.018 0.018 0.084 0.084
## 395 Im22 ~~ C_CR1 1.256 -0.058 -0.058 -0.075 -0.075
## 396 Im12 ~~ COM_A4 1.239 -0.037 -0.037 -0.072 -0.072
## 397 RI =~ COM_A4 1.230 0.093 0.055 0.032 0.032
## 398 Im20 ~~ C_REP3 1.225 -0.018 -0.018 -0.059 -0.059
## 399 Im3 ~~ Im10 1.223 0.011 0.011 0.070 0.070
## 400 PRODQUAL =~ COM_A2 1.213 -0.078 -0.055 -0.035 -0.035
## 401 FRENCH =~ SAT_3 1.209 0.051 0.050 0.044 0.044
## 402 Im10 ~~ C_CR4 1.207 -0.027 -0.027 -0.067 -0.067
## 403 Im4 ~~ COM_A4 1.202 -0.027 -0.027 -0.089 -0.089
## 404 PRODQUAL =~ Im20 1.186 0.083 0.058 0.039 0.039
## 405 PROF ~~ AFCOM 1.182 0.034 0.040 0.040 0.040
## 406 CHOICE =~ SAT_1 1.178 0.035 0.046 0.045 0.045
## 407 COI =~ Im20 1.152 -0.031 -0.051 -0.034 -0.034
## 408 PRODQUAL =~ Im22 1.149 -0.083 -0.058 -0.038 -0.038
## 409 Im10 ~~ C_REP3 1.147 -0.007 -0.007 -0.060 -0.060
## 410 SAT_1 ~~ C_CR3 1.144 -0.042 -0.042 -0.070 -0.070
## 411 COI =~ SAT_2 1.136 0.020 0.034 0.034 0.034
## 412 Im16 ~~ Im7 1.135 -0.030 -0.030 -0.098 -0.098
## 413 PRODQUAL =~ Im19 1.134 0.088 0.062 0.055 0.055
## 414 Im1 ~~ COM_A3 1.105 -0.029 -0.029 -0.113 -0.113
## 415 Im16 ~~ C_CR1 1.098 0.052 0.052 0.064 0.064
## 416 Im4 ~~ Im7 1.087 -0.018 -0.018 -0.137 -0.137
## 417 Im17 ~~ COM_A3 1.087 0.031 0.031 0.108 0.108
## 418 PROF =~ Im7 1.079 -0.065 -0.059 -0.049 -0.049
## 419 BRAND =~ Im11 1.044 -0.046 -0.055 -0.048 -0.048
## 420 PROF =~ COM_A1 1.028 0.055 0.050 0.035 0.035
## 421 Im1 ~~ COM_A2 1.000 0.027 0.027 0.108 0.108
## 422 Im6 ~~ SAT_1 0.995 0.022 0.022 0.062 0.062
## 423 Im13 ~~ C_CR3 0.995 -0.046 -0.046 -0.063 -0.063
## 424 Im14 ~~ Im12 0.989 -0.013 -0.013 -0.089 -0.089
## 425 COM_A4 ~~ C_CR3 0.982 -0.063 -0.063 -0.059 -0.059
## 426 SAT_3 ~~ C_REP3 0.980 0.016 0.016 0.049 0.049
## 427 Im1 ~~ Im18 0.980 0.021 0.021 0.104 0.104
## 428 CHOICE =~ Im16 0.965 0.048 0.063 0.052 0.052
## 429 CHOICE =~ Im19 0.965 -0.050 -0.065 -0.058 -0.058
## 430 ATMOS =~ Im2 0.957 -0.032 -0.040 -0.031 -0.031
## 431 Im16 ~~ COM_A3 0.956 0.040 0.040 0.054 0.054
## 432 Im20 ~~ Im18 0.950 0.032 0.032 0.054 0.054
## 433 Im17 ~~ COM_A4 0.902 -0.028 -0.028 -0.101 -0.101
## 434 Im5 ~~ Im2 0.897 -0.023 -0.023 -0.047 -0.047
## 435 Im13 ~~ Im18 0.892 -0.025 -0.025 -0.056 -0.056
## 436 BRAND =~ SAT_3 0.890 -0.037 -0.045 -0.040 -0.040
## 437 ATMOS =~ Im3 0.886 0.024 0.029 0.022 0.022
## 438 ATMOS =~ C_CR3 0.882 -0.050 -0.063 -0.031 -0.031
## 439 CHOICE ~~ SAT 0.882 -0.110 -0.128 -0.128 -0.128
## 440 Im1 ~~ Im2 0.880 1.034 1.034 6.695 6.695
## 441 SAT =~ Im21 0.870 0.051 0.044 0.032 0.032
## 442 Im11 ~~ COM_A2 0.868 0.038 0.038 0.048 0.048
## 443 FOOD =~ Im20 0.862 -0.054 -0.044 -0.029 -0.029
## 444 Im17 ~~ C_REP3 0.860 0.010 0.010 0.090 0.090
## 445 SAT =~ Im1 0.859 -0.049 -0.043 -0.032 -0.032
## 446 ATMOS ~~ SAT 0.859 0.034 0.041 0.041 0.041
## 447 Im7 ~~ COM_A4 0.857 0.031 0.031 0.087 0.087
## 448 Im11 ~~ C_CR4 0.857 0.051 0.051 0.048 0.048
## 449 DECO =~ C_REP2 0.849 -0.014 -0.017 -0.027 -0.027
## 450 Im6 ~~ C_CR4 0.847 -0.041 -0.041 -0.051 -0.051
## 451 Im3 ~~ SAT_1 0.845 0.015 0.015 0.061 0.061
## 452 DECO =~ SAT_2 0.832 0.026 0.033 0.033 0.033
## 453 Im19 ~~ SAT_3 0.832 -0.029 -0.029 -0.052 -0.052
## 454 Im16 ~~ COM_A4 0.828 -0.037 -0.037 -0.052 -0.052
## 455 Im6 ~~ COM_A1 0.825 0.029 0.029 0.048 0.048
## 456 Im6 ~~ C_REP2 0.824 0.010 0.010 0.081 0.081
## 457 BRAND =~ Im1 0.818 -0.039 -0.047 -0.035 -0.035
## 458 Im4 ~~ C_CR3 0.817 0.029 0.029 0.074 0.074
## 459 Im4 ~~ COM_A2 0.807 -0.021 -0.021 -0.071 -0.071
## 460 COI =~ SAT_3 0.791 -0.024 -0.040 -0.035 -0.035
## 461 Im7 ~~ C_CR4 0.785 0.038 0.038 0.082 0.082
## 462 SAT_2 ~~ C_REP3 0.783 0.010 0.010 0.048 0.048
## 463 BRAND =~ COM_A4 0.778 -0.037 -0.045 -0.026 -0.026
## 464 Im16 ~~ SAT_2 0.778 0.024 0.024 0.052 0.052
## 465 Im20 ~~ Im12 0.776 0.026 0.026 0.058 0.058
## 466 PROF =~ Im18 0.772 -0.078 -0.071 -0.051 -0.051
## 467 PROF =~ Im17 0.772 0.079 0.072 0.058 0.058
## 468 FOOD =~ SAT_3 0.770 0.050 0.040 0.036 0.036
## 469 COI =~ Im5 0.767 0.022 0.037 0.028 0.028
## 470 Im17 ~~ C_REP2 0.767 0.009 0.009 0.155 0.155
## 471 Im7 ~~ C_CR1 0.757 -0.035 -0.035 -0.087 -0.087
## 472 FRENCH =~ COM_A1 0.751 -0.042 -0.042 -0.029 -0.029
## 473 CHOICE =~ C_REP2 0.751 -0.012 -0.016 -0.026 -0.026
## 474 Im14 ~~ SAT_1 0.748 -0.010 -0.010 -0.075 -0.075
## 475 Im21 ~~ Im11 0.737 -0.032 -0.032 -0.043 -0.043
## 476 Im3 ~~ Im19 0.732 0.016 0.016 0.055 0.055
## 477 PROF =~ Im11 0.726 0.054 0.049 0.043 0.043
## 478 BRAND =~ Im2 0.725 0.033 0.039 0.031 0.031
## 479 Im12 ~~ COM_A3 0.724 -0.028 -0.028 -0.054 -0.054
## 480 Im1 ~~ C_REP2 0.720 0.008 0.008 0.154 0.154
## 481 Im14 ~~ Im13 0.716 0.012 0.012 0.072 0.072
## 482 Im20 ~~ Im2 0.715 -0.021 -0.021 -0.047 -0.047
## 483 Im2 ~~ C_REP3 0.715 0.009 0.009 0.043 0.043
## 484 BRAND =~ COM_A2 0.713 -0.034 -0.041 -0.026 -0.026
## 485 Im5 ~~ C_CR3 0.707 -0.045 -0.045 -0.045 -0.045
## 486 Im7 ~~ C_REP3 0.706 0.010 0.010 0.071 0.071
## 487 Im5 ~~ C_CR4 0.704 0.044 0.044 0.044 0.044
## 488 COM_A3 ~~ SAT_3 0.702 -0.037 -0.037 -0.044 -0.044
## 489 Im21 ~~ Im17 0.698 0.022 0.022 0.085 0.085
## 490 Im3 ~~ C_CR4 0.696 -0.027 -0.027 -0.049 -0.049
## 491 Im12 ~~ COM_A2 0.654 0.026 0.026 0.052 0.052
## 492 FOOD =~ COM_A2 0.653 -0.047 -0.038 -0.024 -0.024
## 493 COM_A4 ~~ C_REP3 0.652 -0.014 -0.014 -0.043 -0.043
## 494 PRODQUAL =~ SAT_1 0.651 -0.042 -0.029 -0.029 -0.029
## 495 Im21 ~~ C_REP1 0.650 -0.015 -0.015 -0.041 -0.041
## 496 Im4 ~~ Im5 0.638 0.028 0.028 0.099 0.099
## 497 ATMOS =~ Im1 0.638 0.029 0.036 0.027 0.027
## 498 BRAND =~ Im14 0.638 0.015 0.018 0.021 0.021
## 499 BRAND =~ Im10 0.638 -0.015 -0.018 -0.020 -0.020
## 500 FRENCH =~ Im13 0.638 -0.033 -0.033 -0.027 -0.027
## 501 AFCOM =~ C_REP2 0.636 -0.012 -0.014 -0.022 -0.022
## 502 SAT ~ PRODQUAL 0.629 0.055 0.045 0.045 0.045
## 503 PRODQUAL =~ COM_A3 0.623 0.058 0.041 0.025 0.025
## 504 SAT =~ Im14 0.623 0.020 0.018 0.021 0.021
## 505 PRODQUAL ~ SAT 0.621 -0.038 -0.047 -0.047 -0.047
## 506 ATMOS =~ Im19 0.620 -0.034 -0.043 -0.038 -0.038
## 507 Im4 ~~ Im10 0.613 -0.008 -0.008 -0.067 -0.067
## 508 Im2 ~~ COM_A4 0.612 0.022 0.022 0.043 0.043
## 509 RI =~ Im1 0.609 -0.046 -0.027 -0.020 -0.020
## 510 Im10 ~~ Im2 0.608 -0.009 -0.009 -0.045 -0.045
## 511 Im10 ~~ COM_A3 0.603 -0.015 -0.015 -0.046 -0.046
## 512 ATMOS =~ COM_A3 0.600 0.039 0.048 0.030 0.030
## 513 Im12 ~~ C_CR1 0.600 -0.031 -0.031 -0.054 -0.054
## 514 FOOD ~~ SAT 0.598 0.017 0.032 0.032 0.032
## 515 COM_A2 ~~ C_CR4 0.598 -0.046 -0.046 -0.044 -0.044
## 516 Im22 ~~ Im13 0.597 -0.024 -0.024 -0.051 -0.051
## 517 Im10 ~~ COM_A1 0.593 -0.014 -0.014 -0.045 -0.045
## 518 RI =~ Im4 0.589 -0.034 -0.020 -0.015 -0.015
## 519 Im21 ~~ Im12 0.585 0.022 0.022 0.047 0.047
## 520 Im7 ~~ C_REP1 0.583 0.011 0.011 0.065 0.065
## 521 SAT_3 ~~ C_CR1 0.582 0.041 0.041 0.044 0.044
## 522 Im4 ~~ C_CR4 0.581 0.024 0.024 0.061 0.061
## 523 Im7 ~~ COM_A3 0.566 0.025 0.025 0.068 0.068
## 524 Im20 ~~ Im7 0.551 0.022 0.022 0.070 0.070
## 525 Im14 ~~ Im22 0.549 -0.012 -0.012 -0.063 -0.063
## 526 Im10 ~~ Im21 0.543 -0.012 -0.012 -0.043 -0.043
## 527 Im4 ~~ Im16 0.541 0.015 0.015 0.059 0.059
## 528 PROF =~ Im22 0.532 0.048 0.043 0.028 0.028
## 529 COI =~ Im3 0.531 0.011 0.019 0.014 0.014
## 530 FRENCH =~ Im21 0.520 -0.034 -0.034 -0.025 -0.025
## 531 Im22 ~~ Im6 0.520 0.022 0.022 0.043 0.043
## 532 Im6 ~~ COM_A3 0.519 -0.025 -0.025 -0.039 -0.039
## 533 Im7 ~~ SAT_1 0.513 0.015 0.015 0.074 0.074
## 534 Im22 ~~ Im16 0.512 0.026 0.026 0.043 0.043
## 535 PRODQUAL =~ C_REP2 0.505 0.020 0.014 0.022 0.022
## 536 Im14 ~~ COM_A4 0.504 0.013 0.013 0.056 0.056
## 537 Im11 ~~ Im18 0.501 0.023 0.023 0.035 0.035
## 538 SAT =~ C_CR3 0.500 -0.053 -0.046 -0.022 -0.022
## 539 Im17 ~~ SAT_3 0.500 -0.019 -0.019 -0.070 -0.070
## 540 Im5 ~~ Im11 0.498 0.026 0.026 0.033 0.033
## 541 Im20 ~~ C_CR3 0.491 -0.040 -0.040 -0.042 -0.042
## 542 Im3 ~~ Im7 0.490 -0.012 -0.012 -0.067 -0.067
## 543 Im10 ~~ Im20 0.488 0.012 0.012 0.043 0.043
## 544 CHOICE =~ C_CR1 0.484 -0.031 -0.041 -0.021 -0.021
## 545 Im14 ~~ Im20 0.479 -0.012 -0.012 -0.055 -0.055
## 546 Im12 ~~ Im2 0.478 -0.013 -0.013 -0.043 -0.043
## 547 Im5 ~~ Im10 0.477 -0.011 -0.011 -0.038 -0.038
## 548 Im21 ~~ Im7 0.471 -0.020 -0.020 -0.061 -0.061
## 549 Im1 ~~ C_CR1 0.468 -0.023 -0.023 -0.082 -0.082
## 550 Im10 ~~ SAT_1 0.467 0.008 0.008 0.047 0.047
## 551 Im2 ~~ COM_A1 0.467 -0.018 -0.018 -0.036 -0.036
## 552 PRODQUAL =~ Im14 0.462 0.027 0.019 0.022 0.022
## 553 PRODQUAL =~ Im10 0.462 -0.026 -0.018 -0.021 -0.021
## 554 Im5 ~~ Im21 0.461 -0.025 -0.025 -0.034 -0.034
## 555 Im12 ~~ SAT_2 0.459 -0.014 -0.014 -0.045 -0.045
## 556 COI =~ Im16 0.453 -0.018 -0.030 -0.025 -0.025
## 557 PRODQUAL =~ C_REP1 0.445 0.022 0.016 0.021 0.021
## 558 BRAND =~ Im19 0.445 0.034 0.040 0.036 0.036
## 559 C_CR1 ~~ C_CR4 0.442 -0.240 -0.240 -0.200 -0.200
## 560 PROF =~ Im3 0.441 0.032 0.029 0.022 0.022
## 561 COM_A1 ~~ C_REP1 0.435 -0.013 -0.013 -0.034 -0.034
## 562 AFCOM =~ Im13 0.435 -0.023 -0.026 -0.021 -0.021
## 563 AFCOM =~ C_CR3 0.434 0.038 0.042 0.020 0.020
## 564 Im19 ~~ SAT_2 0.434 0.015 0.015 0.043 0.043
## 565 CHOICE =~ Im4 0.434 -0.015 -0.019 -0.014 -0.014
## 566 Im12 ~~ C_REP3 0.433 -0.008 -0.008 -0.039 -0.039
## 567 PROF =~ Im6 0.430 0.035 0.032 0.027 0.027
## 568 COI =~ COM_A3 0.429 0.020 0.032 0.020 0.020
## 569 CHOICE =~ Im11 0.426 -0.025 -0.032 -0.028 -0.028
## 570 Im1 ~~ Im16 0.420 -0.016 -0.016 -0.072 -0.072
## 571 CHOICE =~ Im3 0.410 -0.014 -0.019 -0.014 -0.014
## 572 SAT_1 ~~ C_REP2 0.407 -0.006 -0.006 -0.066 -0.066
## 573 Im6 ~~ SAT_3 0.403 -0.020 -0.020 -0.033 -0.033
## 574 Im13 ~~ Im6 0.401 0.016 0.016 0.038 0.038
## 575 AFCOM =~ Im4 0.399 -0.015 -0.016 -0.012 -0.012
## 576 RI =~ COM_A2 0.395 -0.050 -0.029 -0.018 -0.018
## 577 C_CR3 ~~ C_CR4 0.394 -0.226 -0.226 -0.165 -0.165
## 578 Im20 ~~ C_REP1 0.388 -0.012 -0.012 -0.033 -0.033
## 579 Im11 ~~ C_CR3 0.385 0.035 0.035 0.033 0.033
## 580 FRENCH =~ SAT_2 0.383 0.021 0.020 0.020 0.020
## 581 Im12 ~~ C_REP2 0.378 0.007 0.007 0.065 0.065
## 582 Im10 ~~ SAT_3 0.377 0.011 0.011 0.035 0.035
## 583 ATMOS ~ SAT 0.371 -0.052 -0.036 -0.036 -0.036
## 584 Im13 ~~ Im19 0.371 0.016 0.016 0.040 0.040
## 585 DECO =~ SAT_3 0.370 -0.023 -0.028 -0.025 -0.025
## 586 Im2 ~~ Im7 0.369 0.012 0.012 0.053 0.053
## 587 SAT_2 ~~ C_REP2 0.368 0.006 0.006 0.058 0.058
## 588 Im14 ~~ C_REP2 0.367 -0.004 -0.004 -0.078 -0.078
## 589 AFCOM =~ Im6 0.367 0.022 0.025 0.021 0.021
## 590 COM_A1 ~~ C_CR4 0.359 -0.034 -0.034 -0.033 -0.033
## 591 Im1 ~~ SAT_3 0.354 0.015 0.015 0.061 0.061
## 592 FOOD =~ Im3 0.352 -0.021 -0.017 -0.013 -0.013
## 593 Im6 ~~ COM_A2 0.352 0.020 0.020 0.033 0.033
## 594 ATMOS =~ Im16 0.351 -0.027 -0.033 -0.028 -0.028
## 595 Im5 ~~ Im22 0.351 0.022 0.022 0.033 0.033
## 596 PRODQUAL =~ COM_A1 0.350 0.040 0.028 0.020 0.020
## 597 C_REP2 ~~ C_CR3 0.348 0.012 0.012 0.056 0.056
## 598 Im17 ~~ COM_A2 0.346 -0.017 -0.017 -0.061 -0.061
## 599 Im5 ~~ Im17 0.344 0.015 0.015 0.056 0.056
## 600 Im11 ~~ C_REP3 0.343 0.009 0.009 0.028 0.028
## 601 COM_A3 ~~ SAT_1 0.342 0.018 0.018 0.037 0.037
## 602 CHOICE =~ COM_A4 0.338 -0.022 -0.029 -0.017 -0.017
## 603 Im3 ~~ COM_A2 0.336 -0.014 -0.014 -0.034 -0.034
## 604 Im3 ~~ COM_A1 0.336 -0.013 -0.013 -0.033 -0.033
## 605 Im17 ~~ C_CR1 0.333 -0.021 -0.021 -0.067 -0.067
## 606 FRENCH =~ Im3 0.330 -0.016 -0.016 -0.012 -0.012
## 607 Im6 ~~ C_CR1 0.326 0.024 0.024 0.034 0.034
## 608 Im11 ~~ COM_A1 0.321 -0.022 -0.022 -0.028 -0.028
## 609 COM_A4 ~~ SAT_2 0.316 0.018 0.018 0.034 0.034
## 610 SAT_2 ~~ C_CR1 0.314 -0.021 -0.021 -0.036 -0.036
## 611 FRENCH =~ COM_A4 0.312 0.031 0.030 0.018 0.018
## 612 Im3 ~~ Im13 0.310 0.010 0.010 0.035 0.035
## 613 Im19 ~~ C_CR3 0.309 0.025 0.025 0.035 0.035
## 614 CHOICE =~ C_CR3 0.303 -0.026 -0.035 -0.017 -0.017
## 615 Im3 ~~ SAT_2 0.303 -0.009 -0.009 -0.034 -0.034
## 616 Im13 ~~ Im7 0.303 -0.014 -0.014 -0.055 -0.055
## 617 Im5 ~~ C_REP2 0.302 -0.007 -0.007 -0.046 -0.046
## 618 Im17 ~~ Im7 0.301 -0.012 -0.012 -0.099 -0.099
## 619 Im18 ~~ SAT_1 0.296 -0.012 -0.012 -0.033 -0.033
## 620 Im19 ~~ C_CR1 0.292 0.023 0.023 0.036 0.036
## 621 Im21 ~~ Im13 0.288 -0.017 -0.017 -0.032 -0.032
## 622 AFCOM =~ Im7 0.287 -0.022 -0.024 -0.020 -0.020
## 623 AFCOM =~ Im14 0.284 0.010 0.011 0.013 0.013
## 624 COM_A1 ~~ C_CR1 0.282 -0.028 -0.028 -0.031 -0.031
## 625 Im4 ~~ Im14 0.279 0.005 0.005 0.058 0.058
## 626 Im5 ~~ Im20 0.279 0.020 0.020 0.028 0.028
## 627 COI =~ C_REP3 0.279 -0.006 -0.010 -0.017 -0.017
## 628 Im17 ~~ C_CR3 0.278 0.021 0.021 0.057 0.057
## 629 Im21 ~~ COM_A4 0.277 -0.023 -0.023 -0.029 -0.029
## 630 CHOICE =~ Im17 0.275 0.022 0.028 0.023 0.023
## 631 CHOICE =~ Im18 0.275 -0.021 -0.028 -0.020 -0.020
## 632 Im22 ~~ COM_A2 0.272 0.021 0.021 0.032 0.032
## 633 Im2 ~~ C_CR4 0.271 -0.019 -0.019 -0.029 -0.029
## 634 Im21 ~~ Im16 0.271 -0.019 -0.019 -0.028 -0.028
## 635 Im4 ~~ C_REP3 0.271 -0.005 -0.005 -0.038 -0.038
## 636 COI =~ Im6 0.265 -0.011 -0.018 -0.015 -0.015
## 637 Im7 ~~ SAT_2 0.262 -0.011 -0.011 -0.049 -0.049
## 638 CHOICE =~ Im6 0.256 -0.014 -0.019 -0.016 -0.016
## 639 Im17 ~~ SAT_2 0.247 0.009 0.009 0.054 0.054
## 640 Im20 ~~ Im19 0.247 0.016 0.016 0.031 0.031
## 641 COI =~ Im12 0.243 0.011 0.018 0.016 0.016
## 642 DECO =~ SAT_1 0.242 -0.015 -0.018 -0.018 -0.018
## 643 SAT =~ Im6 0.242 0.022 0.019 0.016 0.016
## 644 Im16 ~~ C_REP1 0.239 0.009 0.009 0.025 0.025
## 645 Im18 ~~ C_REP2 0.237 -0.006 -0.006 -0.043 -0.043
## 646 DECO =~ Im11 0.231 0.019 0.024 0.021 0.021
## 647 SAT_3 ~~ C_REP1 0.230 -0.009 -0.009 -0.024 -0.024
## 648 Im10 ~~ Im19 0.230 -0.007 -0.007 -0.032 -0.032
## 649 DECO =~ COM_A4 0.229 0.019 0.024 0.014 0.014
## 650 Im4 ~~ SAT_1 0.225 -0.007 -0.007 -0.043 -0.043
## 651 Im14 ~~ C_REP1 0.224 0.004 0.004 0.034 0.034
## 652 PROF =~ C_REP2 0.222 -0.011 -0.010 -0.016 -0.016
## 653 Im20 ~~ SAT_3 0.218 0.018 0.018 0.025 0.025
## 654 SAT_3 ~~ C_CR4 0.215 0.026 0.026 0.025 0.025
## 655 Im16 ~~ Im18 0.213 -0.014 -0.014 -0.025 -0.025
## 656 Im11 ~~ SAT_2 0.212 -0.013 -0.013 -0.025 -0.025
## 657 FOOD =~ COM_A4 0.212 -0.028 -0.023 -0.013 -0.013
## 658 PROF =~ SAT_3 0.209 -0.033 -0.030 -0.026 -0.026
## 659 Im21 ~~ SAT_1 0.208 0.012 0.012 0.028 0.028
## 660 Im21 ~~ SAT_2 0.207 -0.012 -0.012 -0.026 -0.026
## 661 Im22 ~~ Im17 0.206 0.012 0.012 0.053 0.053
## 662 Im5 ~~ SAT_1 0.205 -0.012 -0.012 -0.026 -0.026
## 663 AFCOM =~ SAT_3 0.204 0.020 0.023 0.020 0.020
## 664 Im3 ~~ C_REP2 0.199 -0.004 -0.004 -0.043 -0.043
## 665 Im4 ~~ C_REP2 0.198 0.004 0.004 0.058 0.058
## 666 SAT =~ COM_A4 0.197 0.030 0.026 0.015 0.015
## 667 PRODQUAL =~ C_CR3 0.195 -0.041 -0.029 -0.014 -0.014
## 668 Im12 ~~ C_CR3 0.194 0.019 0.019 0.029 0.029
## 669 SAT =~ Im7 0.191 0.021 0.018 0.015 0.015
## 670 Im11 ~~ C_CR1 0.188 -0.023 -0.023 -0.024 -0.024
## 671 Im13 ~~ COM_A1 0.187 0.014 0.014 0.025 0.025
## 672 Im6 ~~ C_REP1 0.185 -0.007 -0.007 -0.022 -0.022
## 673 RI =~ Im20 0.180 -0.036 -0.021 -0.014 -0.014
## 674 Im4 ~~ COM_A1 0.174 0.009 0.009 0.032 0.032
## 675 BRAND =~ Im21 0.174 -0.018 -0.022 -0.016 -0.016
## 676 AFCOM =~ Im18 0.174 -0.015 -0.017 -0.012 -0.012
## 677 Im5 ~~ COM_A3 0.173 -0.017 -0.017 -0.021 -0.021
## 678 AFCOM =~ SAT_1 0.171 -0.015 -0.016 -0.016 -0.016
## 679 Im21 ~~ Im2 0.169 0.010 0.010 0.022 0.022
## 680 Im21 ~~ Im19 0.169 -0.013 -0.013 -0.024 -0.024
## 681 Im16 ~~ C_REP2 0.168 -0.006 -0.006 -0.038 -0.038
## 682 COM_A4 ~~ C_CR1 0.167 0.024 0.024 0.025 0.025
## 683 COM_A2 ~~ C_REP3 0.164 -0.007 -0.007 -0.021 -0.021
## 684 Im20 ~~ Im11 0.164 0.016 0.016 0.021 0.021
## 685 Im22 ~~ C_CR3 0.164 0.023 0.023 0.026 0.026
## 686 ATMOS =~ SAT_1 0.163 0.011 0.014 0.014 0.014
## 687 RI =~ Im18 0.162 -0.027 -0.016 -0.011 -0.011
## 688 RI =~ Im17 0.162 0.027 0.016 0.013 0.013
## 689 DECO ~~ AFCOM 0.161 0.017 0.015 0.015 0.015
## 690 Im1 ~~ C_CR3 0.161 -0.015 -0.015 -0.045 -0.045
## 691 Im16 ~~ COM_A1 0.154 -0.015 -0.015 -0.021 -0.021
## 692 Im12 ~~ Im19 0.151 0.009 0.009 0.027 0.027
## 693 Im10 ~~ Im22 0.151 0.007 0.007 0.026 0.026
## 694 Im22 ~~ COM_A4 0.151 0.017 0.017 0.024 0.024
## 695 Im14 ~~ Im11 0.150 0.006 0.006 0.027 0.027
## 696 Im2 ~~ Im6 0.146 -0.008 -0.008 -0.020 -0.020
## 697 Im14 ~~ Im1 0.145 -0.004 -0.004 -0.058 -0.058
## 698 Im3 ~~ C_REP1 0.142 0.004 0.004 0.021 0.021
## 699 RI =~ C_CR3 0.140 0.041 0.024 0.012 0.012
## 700 Im21 ~~ C_REP2 0.139 -0.005 -0.005 -0.033 -0.033
## 701 SAT =~ Im10 0.138 -0.010 -0.008 -0.010 -0.010
## 702 FOOD =~ Im19 0.138 -0.024 -0.020 -0.017 -0.017
## 703 BRAND =~ SAT_1 0.137 -0.011 -0.013 -0.013 -0.013
## 704 Im4 ~~ Im13 0.137 -0.007 -0.007 -0.032 -0.032
## 705 FOOD =~ COM_A1 0.137 -0.021 -0.017 -0.012 -0.012
## 706 PROF =~ C_CR3 0.136 -0.027 -0.024 -0.012 -0.012
## 707 Im4 ~~ Im20 0.136 0.008 0.008 0.030 0.030
## 708 Im13 ~~ C_CR1 0.134 -0.016 -0.016 -0.024 -0.024
## 709 Im17 ~~ Im6 0.133 0.008 0.008 0.037 0.037
## 710 Im3 ~~ C_CR3 0.132 -0.012 -0.012 -0.022 -0.022
## 711 Im19 ~~ Im6 0.132 -0.009 -0.009 -0.021 -0.021
## 712 Im2 ~~ C_CR3 0.128 0.013 0.013 0.020 0.020
## 713 Im12 ~~ Im18 0.126 -0.009 -0.009 -0.022 -0.022
## 714 FOOD =~ Im4 0.124 -0.013 -0.010 -0.008 -0.008
## 715 RI =~ Im2 0.123 0.018 0.011 0.008 0.008
## 716 Im17 ~~ SAT_1 0.123 0.006 0.006 0.041 0.041
## 717 Im19 ~~ C_CR4 0.122 0.016 0.016 0.021 0.021
## 718 DECO ~ SAT 0.119 -0.057 -0.040 -0.040 -0.040
## 719 Im1 ~~ Im7 0.119 -0.007 -0.007 -0.063 -0.063
## 720 Im19 ~~ Im7 0.119 0.009 0.009 0.036 0.036
## 721 FRENCH =~ Im17 0.118 -0.014 -0.014 -0.011 -0.011
## 722 FRENCH =~ Im18 0.118 0.014 0.014 0.010 0.010
## 723 Im4 ~~ Im19 0.113 -0.006 -0.006 -0.030 -0.030
## 724 Im16 ~~ SAT_3 0.111 0.012 0.012 0.018 0.018
## 725 SAT =~ C_REP3 0.109 0.007 0.006 0.011 0.011
## 726 FOOD =~ Im21 0.109 0.018 0.015 0.011 0.011
## 727 COM_A3 ~~ C_CR4 0.109 -0.020 -0.020 -0.019 -0.019
## 728 Im18 ~~ C_CR3 0.109 -0.016 -0.016 -0.018 -0.018
## 729 AFCOM =~ Im19 0.108 0.012 0.013 0.012 0.012
## 730 AFCOM =~ Im1 0.108 -0.009 -0.010 -0.008 -0.008
## 731 COI =~ COM_A1 0.107 0.009 0.015 0.010 0.010
## 732 Im3 ~~ Im6 0.106 0.006 0.006 0.019 0.019
## 733 Im21 ~~ Im1 0.105 0.008 0.008 0.034 0.034
## 734 Im21 ~~ COM_A1 0.101 0.012 0.012 0.017 0.017
## 735 COI =~ Im7 0.100 -0.008 -0.013 -0.011 -0.011
## 736 Im17 ~~ C_CR4 0.098 0.012 0.012 0.033 0.033
## 737 CHOICE =~ SAT_3 0.098 0.012 0.016 0.014 0.014
## 738 COI =~ Im14 0.098 -0.004 -0.006 -0.007 -0.007
## 739 COI =~ Im10 0.098 0.004 0.006 0.007 0.007
## 740 FOOD =~ Im22 0.098 0.018 0.015 0.010 0.010
## 741 Im6 ~~ C_REP3 0.097 -0.004 -0.004 -0.016 -0.016
## 742 SAT =~ Im3 0.097 0.010 0.009 0.007 0.007
## 743 Im10 ~~ C_REP2 0.097 -0.002 -0.002 -0.031 -0.031
## 744 Im12 ~~ COM_A1 0.096 0.009 0.009 0.019 0.019
## 745 Im21 ~~ C_CR1 0.096 0.016 0.016 0.018 0.018
## 746 RI =~ Im6 0.094 0.019 0.011 0.010 0.010
## 747 C_REP3 ~~ C_CR1 0.093 0.007 0.007 0.017 0.017
## 748 ATMOS =~ Im6 0.092 -0.010 -0.013 -0.011 -0.011
## 749 ATMOS =~ Im7 0.092 0.012 0.015 0.012 0.012
## 750 AFCOM =~ Im10 0.092 -0.006 -0.006 -0.007 -0.007
## 751 DECO ~ AFCOM 0.090 0.015 0.013 0.013 0.013
## 752 ATMOS =~ SAT_3 0.086 -0.011 -0.014 -0.012 -0.012
## 753 Im5 ~~ COM_A4 0.085 -0.012 -0.012 -0.015 -0.015
## 754 Im5 ~~ Im18 0.084 0.009 0.009 0.014 0.014
## 755 AFCOM =~ Im17 0.084 0.009 0.010 0.008 0.008
## 756 Im10 ~~ C_REP1 0.082 0.002 0.002 0.016 0.016
## 757 Im4 ~~ Im21 0.080 0.006 0.006 0.022 0.022
## 758 FRENCH =~ C_CR3 0.077 -0.018 -0.018 -0.009 -0.009
## 759 DECO =~ Im21 0.077 -0.011 -0.014 -0.010 -0.010
## 760 Im6 ~~ SAT_2 0.076 -0.006 -0.006 -0.016 -0.016
## 761 Im22 ~~ COM_A3 0.075 0.012 0.012 0.017 0.017
## 762 FOOD =~ C_CR3 0.073 -0.021 -0.017 -0.008 -0.008
## 763 DECO =~ Im19 0.072 0.016 0.020 0.018 0.018
## 764 DECO =~ Im16 0.072 -0.016 -0.019 -0.016 -0.016
## 765 Im3 ~~ C_REP3 0.072 0.002 0.002 0.015 0.015
## 766 FRENCH =~ Im12 0.071 -0.011 -0.010 -0.009 -0.009
## 767 Im4 ~~ C_REP1 0.070 -0.003 -0.003 -0.020 -0.020
## 768 Im7 ~~ C_CR3 0.068 -0.011 -0.011 -0.025 -0.025
## 769 Im11 ~~ Im19 0.067 -0.008 -0.008 -0.014 -0.014
## 770 Im14 ~~ SAT_3 0.066 -0.004 -0.004 -0.019 -0.019
## 771 SAT =~ Im22 0.065 -0.015 -0.013 -0.008 -0.008
## 772 Im5 ~~ C_CR1 0.065 0.013 0.013 0.014 0.014
## 773 Im5 ~~ COM_A1 0.065 -0.010 -0.010 -0.013 -0.013
## 774 Im10 ~~ C_CR3 0.065 -0.006 -0.006 -0.016 -0.016
## 775 PROF =~ COM_A4 0.063 -0.015 -0.014 -0.008 -0.008
## 776 Im5 ~~ SAT_3 0.061 -0.009 -0.009 -0.012 -0.012
## 777 Im21 ~~ COM_A2 0.060 0.010 0.010 0.013 0.013
## 778 Im16 ~~ Im6 0.060 -0.007 -0.007 -0.013 -0.013
## 779 Im20 ~~ Im16 0.059 0.009 0.009 0.014 0.014
## 780 PROF =~ Im21 0.059 0.015 0.013 0.010 0.010
## 781 Im2 ~~ Im19 0.058 -0.005 -0.005 -0.014 -0.014
## 782 Im5 ~~ Im12 0.058 0.007 0.007 0.014 0.014
## 783 ATMOS =~ Im14 0.057 0.004 0.005 0.006 0.006
## 784 Im1 ~~ Im6 0.057 -0.005 -0.005 -0.025 -0.025
## 785 ATMOS =~ Im10 0.057 -0.004 -0.005 -0.006 -0.006
## 786 Im18 ~~ COM_A3 0.057 -0.009 -0.009 -0.013 -0.013
## 787 Im16 ~~ COM_A2 0.056 0.009 0.009 0.013 0.013
## 788 Im4 ~~ SAT_2 0.055 -0.004 -0.004 -0.020 -0.020
## 789 DECO =~ COM_A1 0.055 -0.009 -0.011 -0.007 -0.007
## 790 RI =~ C_CR1 0.054 -0.024 -0.014 -0.007 -0.007
## 791 Im14 ~~ COM_A1 0.054 0.004 0.004 0.017 0.017
## 792 Im10 ~~ Im1 0.054 -0.003 -0.003 -0.027 -0.027
## 793 COM_A2 ~~ C_REP1 0.052 0.005 0.005 0.012 0.012
## 794 Im20 ~~ C_CR1 0.050 -0.012 -0.012 -0.014 -0.014
## 795 RI =~ Im3 0.041 0.009 0.005 0.004 0.004
## 796 Im14 ~~ C_CR3 0.040 0.005 0.005 0.016 0.016
## 797 SAT_1 ~~ C_REP1 0.040 0.003 0.003 0.012 0.012
## 798 BRAND =~ C_CR3 0.039 -0.010 -0.012 -0.006 -0.006
## 799 RI =~ SAT_1 0.038 0.011 0.006 0.006 0.006
## 800 AFCOM =~ C_CR1 0.037 0.010 0.011 0.006 0.006
## 801 Im6 ~~ COM_A4 0.035 -0.007 -0.007 -0.010 -0.010
## 802 FOOD ~~ AFCOM 0.035 0.005 0.007 0.007 0.007
## 803 SAT =~ C_REP2 0.034 -0.004 -0.003 -0.005 -0.005
## 804 SAT_3 ~~ C_REP2 0.034 -0.003 -0.003 -0.016 -0.016
## 805 PRODQUAL =~ COM_A4 0.032 -0.013 -0.009 -0.006 -0.006
## 806 Im20 ~~ C_CR4 0.031 -0.010 -0.010 -0.010 -0.010
## 807 Im18 ~~ SAT_2 0.030 0.004 0.004 0.010 0.010
## 808 Im18 ~~ COM_A4 0.030 -0.006 -0.006 -0.009 -0.009
## 809 DECO =~ Im2 0.026 0.005 0.006 0.005 0.005
## 810 DECO =~ Im1 0.026 -0.006 -0.007 -0.005 -0.005
## 811 Im14 ~~ Im19 0.026 0.002 0.002 0.014 0.014
## 812 PROF ~ AFCOM 0.026 0.006 0.007 0.007 0.007
## 813 BRAND ~~ SAT 0.025 0.005 0.006 0.006 0.006
## 814 C_REP1 ~~ C_CR4 0.024 0.004 0.004 0.008 0.008
## 815 Im3 ~~ SAT_3 0.024 -0.004 -0.004 -0.009 -0.009
## 816 Im18 ~~ C_CR1 0.022 0.006 0.006 0.009 0.009
## 817 PROF =~ Im10 0.021 0.005 0.005 0.005 0.005
## 818 PROF =~ Im14 0.021 -0.005 -0.005 -0.006 -0.006
## 819 Im19 ~~ C_REP3 0.021 -0.002 -0.002 -0.008 -0.008
## 820 Im19 ~~ COM_A2 0.020 -0.005 -0.005 -0.009 -0.009
## 821 RI =~ SAT_3 0.020 0.011 0.006 0.006 0.006
## 822 BRAND ~~ AFCOM 0.020 -0.006 -0.005 -0.005 -0.005
## 823 RI =~ C_CR4 0.019 -0.015 -0.009 -0.004 -0.004
## 824 Im1 ~~ Im19 0.019 -0.003 -0.003 -0.017 -0.017
## 825 Im1 ~~ C_CR4 0.018 -0.005 -0.005 -0.015 -0.015
## 826 Im12 ~~ Im1 0.018 -0.003 -0.003 -0.017 -0.017
## 827 Im11 ~~ SAT_3 0.018 -0.005 -0.005 -0.006 -0.006
## 828 FRENCH =~ Im4 0.018 0.004 0.004 0.003 0.003
## 829 DECO =~ Im14 0.018 0.003 0.003 0.004 0.004
## 830 DECO =~ Im10 0.018 -0.003 -0.003 -0.004 -0.004
## 831 Im5 ~~ C_REP3 0.015 -0.002 -0.002 -0.006 -0.006
## 832 Im19 ~~ COM_A4 0.014 -0.004 -0.004 -0.007 -0.007
## 833 CHOICE =~ COM_A2 0.013 -0.004 -0.005 -0.003 -0.003
## 834 C_REP2 ~~ C_CR1 0.012 0.002 0.002 0.011 0.011
## 835 C_REP1 ~~ C_CR1 0.012 0.003 0.003 0.006 0.006
## 836 AFCOM =~ Im3 0.012 -0.003 -0.003 -0.002 -0.002
## 837 AFCOM =~ Im22 0.012 -0.006 -0.006 -0.004 -0.004
## 838 Im18 ~~ C_CR4 0.012 -0.005 -0.005 -0.006 -0.006
## 839 FOOD =~ Im17 0.011 0.005 0.004 0.003 0.003
## 840 FOOD =~ Im18 0.011 -0.005 -0.004 -0.003 -0.003
## 841 Im2 ~~ SAT_3 0.010 -0.003 -0.003 -0.005 -0.005
## 842 Im13 ~~ SAT_1 0.010 0.002 0.002 0.007 0.007
## 843 SAT_1 ~~ SAT_2 0.009 0.005 0.005 0.017 0.017
## 844 Im1 ~~ C_REP1 0.009 -0.001 -0.001 -0.009 -0.009
## 845 Im3 ~~ Im16 0.008 -0.002 -0.002 -0.005 -0.005
## 846 COI =~ Im21 0.008 0.002 0.004 0.003 0.003
## 847 Im21 ~~ COM_A3 0.008 -0.004 -0.004 -0.005 -0.005
## 848 CHOICE =~ Im7 0.007 0.003 0.003 0.003 0.003
## 849 COM_A3 ~~ C_CR1 0.007 0.005 0.005 0.005 0.005
## 850 FRENCH ~ AFCOM 0.006 0.006 0.007 0.007 0.007
## 851 Im11 ~~ Im16 0.006 -0.003 -0.003 -0.004 -0.004
## 852 COM_A2 ~~ C_REP2 0.006 0.001 0.001 0.007 0.007
## 853 Im3 ~~ Im21 0.005 -0.002 -0.002 -0.004 -0.004
## 854 SAT_2 ~~ C_CR4 0.005 0.003 0.003 0.004 0.004
## 855 COM_A4 ~~ C_REP2 0.005 -0.001 -0.001 -0.007 -0.007
## 856 PRODQUAL ~~ SAT 0.004 -0.001 -0.003 -0.003 -0.003
## 857 Im21 ~~ Im6 0.003 -0.002 -0.002 -0.003 -0.003
## 858 Im13 ~~ C_REP3 0.003 0.001 0.001 0.003 0.003
## 859 Im16 ~~ Im17 0.003 -0.001 -0.001 -0.006 -0.006
## 860 COM_A2 ~~ C_CR3 0.003 -0.003 -0.003 -0.003 -0.003
## 861 FOOD =~ SAT_1 0.003 -0.002 -0.002 -0.002 -0.002
## 862 FRENCH =~ Im10 0.002 0.002 0.002 0.002 0.002
## 863 FRENCH =~ Im14 0.002 -0.002 -0.002 -0.002 -0.002
## 864 Im22 ~~ C_CR4 0.002 0.003 0.003 0.003 0.003
## 865 Im16 ~~ C_CR3 0.002 -0.002 -0.002 -0.003 -0.003
## 866 PRODQUAL =~ Im3 0.002 0.002 0.001 0.001 0.001
## 867 PRODQUAL =~ Im21 0.001 0.002 0.002 0.001 0.001
## 868 Im6 ~~ C_CR3 0.001 -0.001 -0.001 -0.002 -0.002
## 869 BRAND =~ C_REP2 0.001 0.000 0.001 0.001 0.001
## 870 PRODQUAL =~ SAT_3 0.000 -0.001 -0.001 -0.001 -0.001
## 871 COI =~ Im18 0.000 0.000 -0.001 -0.001 -0.001
## 872 COI =~ Im17 0.000 0.000 0.001 0.001 0.001
## 873 Im4 ~~ SAT_3 0.000 0.000 0.000 -0.001 -0.001
## 874 Im2 ~~ COM_A2 0.000 0.000 0.000 -0.001 -0.001
## 875 Im13 ~~ C_CR4 0.000 0.001 0.001 0.001 0.001
## 876 FRENCH =~ C_REP3 0.000 0.000 0.000 0.000 0.000
## 877 Im19 ~~ COM_A3 0.000 0.000 0.000 0.001 0.001
## 878 Im18 ~~ SAT_3 0.000 0.000 0.000 -0.001 -0.001
## 879 FOOD =~ Im12 0.000 0.000 0.000 0.000 0.000
## 880 FRENCH =~ Im19 0.000 0.000 0.000 0.000 0.000
## 881 BRAND =~ COM_A1 0.000 0.000 0.000 0.000 0.000
## 882 DECO =~ C_CR3 0.000 0.000 0.000 0.000 0.000
## 883 FOOD =~ C_REP3 0.000 0.000 0.000 0.000 0.000
## 884 Im11 ~~ COM_A4 0.000 0.000 0.000 0.000 0.000
## 885 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
## 886 AFCOM =~ Im21 0.000 0.000 0.000 0.000 0.000
# missing Im8, Im15, Im9
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "
# # delete relationships based on regression significance levels
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + CHOICE + PROF
# AFCOM ~ ATMOS + PRODQUAL + FRENCH
#
# RI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# COI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "
# # delete relationships based on regression significance levels
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + CHOICE + PROF
# AFCOM ~ ATMOS + PRODQUAL + FRENCH
#
# RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im8 + Im9
# COI ~ SAT + AFCOM + ATMOS + PRODQUAL
# "
# # delete relationships based on regression significance levels
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
#
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
#
# SAT ~ DECO + CHOICE + PROF
# AFCOM ~ ATMOS + PRODQUAL + FRENCH
#
# RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im8 + Im9
# COI ~ SAT + AFCOM + ATMOS + PRODQUAL
# "
# delete Im8
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4
SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im9
COI ~ SAT + AFCOM + ATMOS + PRODQUAL
"# # linear regression
# lm_SAT_1 <- lm (model_SAT_1, data = survey)
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 147 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 140
##
## Used Total
## Number of observations 537 553
## Number of missing patterns 124
##
## Model Test User Model:
##
## Test statistic 1055.751
## Degrees of freedom 452
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 12060.146
## Degrees of freedom 528
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.948
## Tucker-Lewis Index (TLI) 0.939
##
## Robust Comparative Fit Index (CFI) 0.949
## Robust Tucker-Lewis Index (TLI) 0.940
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -21763.036
## Loglikelihood unrestricted model (H1) -21235.160
##
## Akaike (AIC) 43806.071
## Bayesian (BIC) 44406.111
## Sample-size adjusted Bayesian (SABIC) 43961.704
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.050
## 90 Percent confidence interval - lower 0.046
## 90 Percent confidence interval - upper 0.054
## P-value H_0: RMSEA <= 0.050 0.515
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.050
## 90 Percent confidence interval - lower 0.046
## 90 Percent confidence interval - upper 0.054
## P-value H_0: Robust RMSEA <= 0.050 0.434
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.088
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.239 0.936
## Im4 1.059 0.025 42.081 0.000 1.312 0.970
## Im5 0.817 0.035 23.461 0.000 1.012 0.759
## FOOD =~
## Im10 1.000 0.819 0.926
## Im14 1.010 0.036 28.263 0.000 0.827 0.950
## ATMOS =~
## Im20 1.000 1.255 0.842
## Im21 0.859 0.041 20.713 0.000 1.078 0.788
## Im22 1.073 0.046 23.143 0.000 1.346 0.880
## PRODQUAL =~
## Im11 1.000 0.715 0.623
## Im12 1.390 0.091 15.223 0.000 0.994 0.875
## Im13 1.451 0.102 14.189 0.000 1.037 0.858
## CHOICE =~
## Im1 1.000 1.302 0.979
## Im2 0.885 0.032 27.610 0.000 1.153 0.899
## PROF =~
## Im16 1.000 0.922 0.764
## Im19 1.041 0.058 18.029 0.000 0.960 0.847
## BRAND =~
## Im17 1.000 1.211 0.968
## Im18 0.995 0.041 24.059 0.000 1.205 0.859
## FRENCH =~
## Im6 1.000 0.977 0.815
## Im7 1.187 0.068 17.488 0.000 1.159 0.955
## AFCOM =~
## COM_A1 1.000 1.138 0.795
## COM_A2 1.181 0.056 21.225 0.000 1.345 0.836
## COM_A3 1.168 0.059 19.731 0.000 1.330 0.818
## COM_A4 1.295 0.063 20.526 0.000 1.474 0.846
## SAT =~
## SAT_1 1.000 0.879 0.863
## SAT_2 0.938 0.051 18.563 0.000 0.824 0.819
## SAT_3 0.821 0.055 14.882 0.000 0.721 0.636
## RI =~
## C_REP1 1.000 0.602 0.813
## C_REP2 0.977 0.044 22.009 0.000 0.588 0.938
## C_REP3 0.707 0.038 18.805 0.000 0.426 0.764
## COI =~
## C_CR1 1.000 1.691 0.853
## C_CR3 1.035 0.051 20.133 0.000 1.749 0.834
## C_CR4 0.959 0.049 19.564 0.000 1.621 0.809
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SAT ~
## DECO -0.074 0.045 -1.663 0.096 -0.105 -0.105
## CHOICE 0.119 0.039 3.023 0.003 0.176 0.176
## PROF 0.555 0.082 6.780 0.000 0.582 0.582
## AFCOM ~
## ATMOS 0.420 0.048 8.657 0.000 0.463 0.463
## PRODQUAL -0.031 0.079 -0.392 0.695 -0.019 -0.019
## FRENCH 0.238 0.054 4.367 0.000 0.204 0.204
## RI ~
## SAT 0.183 0.036 5.091 0.000 0.268 0.268
## AFCOM 0.185 0.030 6.226 0.000 0.350 0.350
## ATMOS 0.034 0.026 1.291 0.197 0.071 0.071
## PRODQUAL 0.104 0.044 2.356 0.018 0.124 0.124
## Im9 -0.040 0.020 -2.026 0.043 -0.067 -0.090
## COI ~
## SAT -0.493 0.109 -4.505 0.000 -0.256 -0.256
## AFCOM 0.524 0.090 5.816 0.000 0.353 0.353
## ATMOS 0.103 0.083 1.249 0.212 0.077 0.077
## PRODQUAL 0.078 0.130 0.597 0.551 0.033 0.033
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.421 0.051 8.250 0.000 0.415 0.415
## ATMOS 0.735 0.083 8.873 0.000 0.473 0.473
## PRODQUAL 0.410 0.052 7.893 0.000 0.463 0.463
## CHOICE 0.717 0.080 8.966 0.000 0.445 0.445
## PROF 0.759 0.072 10.523 0.000 0.664 0.664
## BRAND 0.778 0.078 10.012 0.000 0.519 0.519
## FRENCH 0.415 0.064 6.477 0.000 0.343 0.343
## FOOD ~~
## ATMOS 0.303 0.052 5.879 0.000 0.295 0.295
## PRODQUAL 0.267 0.035 7.657 0.000 0.456 0.456
## CHOICE 0.321 0.051 6.320 0.000 0.301 0.301
## PROF 0.390 0.044 8.795 0.000 0.517 0.517
## BRAND 0.322 0.048 6.698 0.000 0.325 0.325
## FRENCH 0.470 0.048 9.877 0.000 0.587 0.587
## ATMOS ~~
## PRODQUAL 0.376 0.054 7.001 0.000 0.419 0.419
## CHOICE 0.738 0.085 8.681 0.000 0.451 0.451
## PROF 0.570 0.069 8.266 0.000 0.492 0.492
## BRAND 0.784 0.082 9.584 0.000 0.516 0.516
## FRENCH 0.413 0.065 6.366 0.000 0.337 0.337
## PRODQUAL ~~
## CHOICE 0.450 0.055 8.187 0.000 0.484 0.484
## PROF 0.355 0.044 8.017 0.000 0.539 0.539
## BRAND 0.491 0.054 9.009 0.000 0.567 0.567
## FRENCH 0.219 0.038 5.699 0.000 0.314 0.314
## CHOICE ~~
## PROF 0.728 0.073 10.016 0.000 0.606 0.606
## BRAND 0.818 0.080 10.202 0.000 0.519 0.519
## FRENCH 0.286 0.061 4.675 0.000 0.225 0.225
## PROF ~~
## BRAND 0.683 0.067 10.138 0.000 0.612 0.612
## FRENCH 0.360 0.053 6.847 0.000 0.400 0.400
## BRAND ~~
## FRENCH 0.387 0.062 6.224 0.000 0.327 0.327
## .RI ~~
## .COI -0.021 0.039 -0.541 0.589 -0.028 -0.028
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.991 0.057 86.928 0.000 4.991 3.772
## .Im4 4.997 0.059 85.283 0.000 4.997 3.693
## .Im5 5.040 0.058 86.464 0.000 5.040 3.777
## .Im10 6.099 0.038 159.490 0.000 6.099 6.897
## .Im14 6.138 0.038 162.690 0.000 6.138 7.057
## .Im20 4.698 0.065 72.814 0.000 4.698 3.154
## .Im21 5.156 0.059 87.039 0.000 5.156 3.765
## .Im22 4.299 0.066 64.747 0.000 4.299 2.811
## .Im11 5.654 0.050 113.388 0.000 5.654 4.927
## .Im12 5.664 0.049 114.654 0.000 5.664 4.985
## .Im13 5.446 0.052 103.878 0.000 5.446 4.507
## .Im1 4.802 0.058 83.327 0.000 4.802 3.609
## .Im2 4.868 0.056 87.545 0.000 4.868 3.794
## .Im16 5.148 0.053 97.757 0.000 5.148 4.267
## .Im19 5.149 0.049 104.731 0.000 5.149 4.544
## .Im17 5.029 0.054 92.714 0.000 5.029 4.018
## .Im18 4.593 0.061 75.161 0.000 4.593 3.275
## .Im6 5.826 0.052 112.318 0.000 5.826 4.863
## .Im7 5.756 0.053 108.978 0.000 5.756 4.742
## .COM_A1 4.302 0.062 69.280 0.000 4.302 3.006
## .COM_A2 3.902 0.070 55.991 0.000 3.902 2.426
## .COM_A3 3.551 0.071 50.259 0.000 3.551 2.184
## .COM_A4 3.470 0.075 45.997 0.000 3.470 1.991
## .SAT_1 5.350 0.044 121.476 0.000 5.350 5.253
## .SAT_2 5.489 0.044 125.780 0.000 5.489 5.451
## .SAT_3 5.470 0.050 108.945 0.000 5.470 4.821
## .C_REP1 4.487 0.106 42.463 0.000 4.487 6.062
## .C_REP2 4.711 0.102 46.242 0.000 4.711 7.514
## .C_REP3 4.822 0.075 64.152 0.000 4.822 8.653
## .C_CR1 2.696 0.086 31.288 0.000 2.696 1.360
## .C_CR3 3.276 0.091 36.102 0.000 3.276 1.562
## .C_CR4 2.798 0.087 32.198 0.000 2.798 1.396
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## .AFCOM 0.000 0.000 0.000
## .SAT 0.000 0.000 0.000
## .RI 0.000 0.000 0.000
## .COI 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.216 0.025 8.660 0.000 0.216 0.123
## .Im4 0.109 0.025 4.415 0.000 0.109 0.060
## .Im5 0.756 0.050 15.054 0.000 0.756 0.424
## .Im10 0.112 0.020 5.722 0.000 0.112 0.143
## .Im14 0.073 0.019 3.817 0.000 0.073 0.097
## .Im20 0.645 0.059 10.924 0.000 0.645 0.290
## .Im21 0.712 0.057 12.568 0.000 0.712 0.380
## .Im22 0.526 0.061 8.684 0.000 0.526 0.225
## .Im11 0.806 0.055 14.608 0.000 0.806 0.612
## .Im12 0.303 0.039 7.856 0.000 0.303 0.235
## .Im13 0.385 0.044 8.739 0.000 0.385 0.263
## .Im1 0.075 0.048 1.552 0.121 0.075 0.042
## .Im2 0.316 0.042 7.483 0.000 0.316 0.192
## .Im16 0.605 0.050 11.990 0.000 0.605 0.416
## .Im19 0.362 0.044 8.332 0.000 0.362 0.282
## .Im17 0.099 0.046 2.165 0.030 0.099 0.063
## .Im18 0.516 0.055 9.338 0.000 0.516 0.262
## .Im6 0.482 0.054 8.987 0.000 0.482 0.336
## .Im7 0.131 0.063 2.076 0.038 0.131 0.089
## .COM_A1 0.752 0.059 12.765 0.000 0.752 0.367
## .COM_A2 0.779 0.067 11.681 0.000 0.779 0.301
## .COM_A3 0.877 0.071 12.321 0.000 0.877 0.332
## .COM_A4 0.862 0.076 11.353 0.000 0.862 0.284
## .SAT_1 0.265 0.034 7.721 0.000 0.265 0.255
## .SAT_2 0.334 0.034 9.801 0.000 0.334 0.330
## .SAT_3 0.767 0.055 14.004 0.000 0.767 0.596
## .C_REP1 0.186 0.016 11.386 0.000 0.186 0.339
## .C_REP2 0.047 0.010 4.593 0.000 0.047 0.121
## .C_REP3 0.129 0.009 13.897 0.000 0.129 0.417
## .C_CR1 1.069 0.115 9.269 0.000 1.069 0.272
## .C_CR3 1.339 0.131 10.208 0.000 1.339 0.304
## .C_CR4 1.391 0.124 11.205 0.000 1.391 0.346
## DECO 1.535 0.109 14.102 0.000 1.000 1.000
## FOOD 0.670 0.051 13.209 0.000 1.000 1.000
## ATMOS 1.575 0.137 11.500 0.000 1.000 1.000
## PRODQUAL 0.511 0.069 7.425 0.000 1.000 1.000
## CHOICE 1.696 0.119 14.308 0.000 1.000 1.000
## PROF 0.850 0.088 9.645 0.000 1.000 1.000
## BRAND 1.467 0.106 13.811 0.000 1.000 1.000
## FRENCH 0.954 0.094 10.143 0.000 1.000 1.000
## .AFCOM 0.894 0.090 9.937 0.000 0.690 0.690
## .SAT 0.458 0.050 9.224 0.000 0.592 0.592
## .RI 0.237 0.022 10.754 0.000 0.653 0.653
## .COI 2.342 0.216 10.822 0.000 0.819 0.819
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI Im9
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.388 NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9
## DECO NaN
## FOOD NaN
## ATMOS NaN
## PRODQUAL NaN
## CHOICE NaN
## PROF NaN
## BRAND NaN
## FRENCH NaN
## AFCOM NaN
## SAT NaN
## RI NaN
## COI NaN
## Im9 NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9
## DECO NaN
## FOOD NaN
## ATMOS NaN
## PRODQUAL NaN
## CHOICE NaN
## PROF NaN
## BRAND NaN
## FRENCH NaN
## AFCOM NaN
## SAT NaN
## RI NaN
## COI NaN
## Im9 NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI
## DECO 1.000
## FOOD NaN 1.000
## ATMOS NaN NaN 1.000
## PRODQUAL NaN NaN NaN 1.000
## CHOICE NaN NaN NaN NaN 1.000
## PROF NaN NaN NaN NaN NaN 1.000
## BRAND NaN NaN NaN NaN NaN NaN 1.000
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1.000
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI
## COI 0.819
## Im9 NaN 1.000
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## FOOD 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## ATMOS 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## PRODQUAL 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## CHOICE 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## PROF 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## BRAND 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## FRENCH 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## AFCOM 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## SAT 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## RI 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## COI 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## Im9 0.7974649 0.8802885 0.70157 0.6300307 0.8828931 0.6509246 0.8373147
## FRENCH AFCOM SAT RI COI Im9
## DECO 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## FOOD 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## ATMOS 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## PRODQUAL 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## CHOICE 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## PROF 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## BRAND 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## FRENCH 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## AFCOM 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## SAT 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## RI 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## COI 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
## Im9 0.7878764 0.6789499 0.6063891 0.7079517 0.6924479 1
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO 1.000
## FOOD 0.415 1.000
## ATMOS 0.473 0.295 1.000
## PRODQUAL 0.463 0.456 0.419 1.000
## CHOICE 0.445 0.301 0.451 0.484 1.000
## PROF 0.664 0.517 0.492 0.539 0.606 1.000
## BRAND 0.519 0.325 0.516 0.567 0.519 0.612 1.000
## FRENCH 0.343 0.587 0.337 0.314 0.225 0.400 0.327 1.000
## AFCOM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.690
## SAT 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.592
## RI 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## COI 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## RI COI Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI 0.653
## COI -0.028 0.819
## Im9 0.000 0.000 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN .
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN .
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI COI Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI .
## COI NaN .
## Im9 NaN NaN .
arrange(modificationindices(SEM_fit),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im9 ~ FRENCH 155.549 0.778 0.760 0.562 0.562
## 2 Im9 ~ PRODQUAL 124.726 0.974 0.696 0.515 0.515
## 3 Im9 ~ RI 108.294 1.802 1.084 0.802 0.802
## 4 Im9 ~ PROF 97.036 0.674 0.622 0.460 0.460
## 5 Im9 ~ ATMOS 69.952 0.412 0.517 0.383 0.383
## 6 Im9 ~ DECO 67.763 0.397 0.491 0.363 0.363
## 7 AFCOM =~ C_REP1 58.127 0.178 0.203 0.274 0.274
## 8 Im9 ~ SAT 51.349 0.513 0.451 0.334 0.334
## 9 C_REP2 ~~ C_REP3 50.422 0.100 0.100 1.270 1.270
## 10 FRENCH ~ Im9 48.798 0.186 0.191 0.258 0.191
## 11 Im9 ~ CHOICE 48.518 0.319 0.415 0.307 0.307
## 12 AFCOM ~ SAT 43.582 0.411 0.317 0.317 0.317
## 13 Im9 ~ AFCOM 43.178 0.355 0.405 0.299 0.299
## 14 SAT ~ AFCOM 42.359 0.225 0.291 0.291 0.291
## 15 AFCOM ~~ SAT 36.005 0.216 0.338 0.338 0.338
## 16 COM_A1 ~~ COM_A2 27.729 0.269 0.269 0.351 0.351
## 17 SAT ~ COI 25.521 0.189 0.363 0.363 0.363
## 18 ATMOS =~ C_REP1 23.246 0.097 0.122 0.164 0.164
## 19 AFCOM ~ RI 21.546 1.182 0.625 0.625 0.625
## 20 BRAND =~ Im13 20.258 0.200 0.243 0.201 0.201
## 21 Im11 ~~ Im13 20.137 -0.185 -0.185 -0.333 -0.333
## 22 SAT ~ RI 17.611 0.447 0.306 0.306 0.306
## 23 RI =~ SAT_2 17.432 0.262 0.158 0.157 0.157
## 24 PRODQUAL ~ Im9 16.287 0.078 0.110 0.148 0.110
## 25 AFCOM =~ C_REP2 14.938 -0.077 -0.087 -0.139 -0.139
## 26 CHOICE =~ Im20 14.443 -0.149 -0.194 -0.130 -0.130
## 27 BRAND =~ Im12 14.126 -0.159 -0.193 -0.170 -0.170
## 28 SAT =~ COM_A3 13.494 0.214 0.188 0.115 0.115
## 29 FOOD =~ Im11 13.323 0.220 0.180 0.157 0.157
## 30 COM_A3 ~~ C_REP1 13.085 0.079 0.079 0.196 0.196
## 31 AFCOM ~ COI 13.071 -0.340 -0.506 -0.506 -0.506
## 32 AFCOM =~ C_REP3 12.962 -0.067 -0.077 -0.138 -0.138
## 33 C_REP1 ~~ C_REP3 12.820 -0.047 -0.047 -0.300 -0.300
## 34 Im21 ~~ Im22 12.672 -0.226 -0.226 -0.369 -0.369
## 35 PROF =~ COM_A3 12.623 0.207 0.191 0.117 0.117
## 36 RI =~ Im22 12.517 -0.298 -0.179 -0.117 -0.117
## 37 SAT ~ FRENCH 12.241 0.149 0.166 0.166 0.166
## 38 C_REP1 ~~ C_REP2 12.220 -0.077 -0.077 -0.820 -0.820
## 39 CHOICE =~ Im13 12.179 0.125 0.163 0.135 0.135
## 40 Im21 ~~ C_REP3 11.752 0.054 0.054 0.178 0.178
## 41 Im11 ~~ Im12 11.626 0.135 0.135 0.272 0.272
## 42 AFCOM =~ SAT_2 11.172 0.096 0.109 0.109 0.109
## 43 ATMOS =~ Im12 10.523 -0.112 -0.141 -0.124 -0.124
## 44 PRODQUAL =~ C_CR4 10.385 0.293 0.209 0.104 0.104
## 45 Im13 ~~ Im1 10.189 0.066 0.066 0.390 0.390
## 46 ATMOS =~ C_REP3 10.184 -0.052 -0.065 -0.116 -0.116
## 47 CHOICE =~ C_REP3 10.055 -0.045 -0.058 -0.105 -0.105
## 48 AFCOM ~ PROF 10.038 0.239 0.194 0.194 0.194
## 49 AFCOM =~ Im11 9.950 0.125 0.142 0.124 0.124
## 50 FRENCH =~ C_REP1 9.836 0.072 0.071 0.095 0.095
## 51 COM_A3 ~~ COM_A4 9.789 0.199 0.199 0.229 0.229
## 52 SAT =~ C_CR4 9.488 0.233 0.205 0.102 0.102
## 53 CHOICE =~ C_REP1 9.465 0.053 0.070 0.094 0.094
## 54 AFCOM ~ CHOICE 9.313 0.134 0.153 0.153 0.153
## 55 Im13 ~~ Im17 9.294 0.068 0.068 0.351 0.351
## 56 Im16 ~~ Im19 9.129 0.290 0.290 0.619 0.619
## 57 PROF ~~ SAT 9.128 -0.155 -0.248 -0.248 -0.248
## 58 PROF ~ SAT 9.128 -0.338 -0.322 -0.322 -0.322
## 59 COM_A1 ~~ COM_A4 8.881 -0.165 -0.165 -0.205 -0.205
## 60 RI =~ COM_A1 8.820 0.257 0.155 0.108 0.108
## 61 COI =~ SAT_2 8.800 0.059 0.100 0.100 0.100
## 62 COI =~ C_REP1 8.762 0.039 0.066 0.089 0.089
## 63 ATMOS =~ C_CR4 8.706 0.156 0.195 0.097 0.097
## 64 Im4 ~~ Im17 8.673 -0.045 -0.045 -0.436 -0.436
## 65 CHOICE =~ Im12 8.589 -0.100 -0.130 -0.114 -0.114
## 66 RI =~ Im21 8.554 0.235 0.142 0.103 0.103
## 67 DECO =~ COM_A3 8.523 0.117 0.145 0.089 0.089
## 68 PRODQUAL =~ C_CR1 8.482 -0.255 -0.182 -0.092 -0.092
## 69 Im19 ~~ C_REP1 8.229 -0.045 -0.045 -0.172 -0.172
## 70 Im1 ~~ SAT_2 7.997 -0.052 -0.052 -0.332 -0.332
## 71 SAT =~ C_REP1 7.972 0.083 0.073 0.098 0.098
## 72 DECO =~ C_REP1 7.871 0.051 0.063 0.085 0.085
## 73 DECO =~ C_CR1 7.663 -0.130 -0.161 -0.081 -0.081
## 74 BRAND =~ COM_A3 7.620 0.115 0.140 0.086 0.086
## 75 DECO ~ SAT 7.414 -0.756 -0.537 -0.537 -0.537
## 76 DECO ~~ SAT 7.413 -0.346 -0.413 -0.413 -0.413
## 77 BRAND =~ Im20 7.321 -0.123 -0.149 -0.100 -0.100
## 78 Im10 ~~ Im6 7.270 -0.038 -0.038 -0.165 -0.165
## 79 PRODQUAL ~~ AFCOM 7.175 -0.129 -0.191 -0.191 -0.191
## 80 PRODQUAL ~ AFCOM 7.175 -0.144 -0.230 -0.230 -0.230
## 81 Im10 ~~ Im16 7.092 0.044 0.044 0.167 0.167
## 82 PROF =~ C_REP3 7.016 -0.059 -0.054 -0.098 -0.098
## 83 FOOD =~ Im6 6.903 -0.283 -0.232 -0.194 -0.194
## 84 ATMOS =~ Im11 6.855 0.104 0.130 0.113 0.113
## 85 Im22 ~~ C_REP3 6.786 -0.041 -0.041 -0.156 -0.156
## 86 SAT =~ Im12 6.784 -0.117 -0.103 -0.090 -0.090
## 87 Im10 ~~ COM_A2 6.714 0.048 0.048 0.162 0.162
## 88 COM_A4 ~~ SAT_1 6.474 0.080 0.080 0.166 0.166
## 89 PRODQUAL =~ Im5 6.361 0.173 0.124 0.093 0.093
## 90 Im14 ~~ Im16 6.314 -0.040 -0.040 -0.191 -0.191
## 91 BRAND =~ Im4 6.299 -0.068 -0.083 -0.061 -0.061
## 92 ATMOS =~ Im5 6.257 0.098 0.122 0.092 0.092
## 93 BRAND =~ Im5 6.249 0.101 0.122 0.091 0.091
## 94 ATMOS ~~ AFCOM 6.160 -0.274 -0.231 -0.231 -0.231
## 95 ATMOS ~ AFCOM 6.160 -0.307 -0.278 -0.278 -0.278
## 96 RI =~ Im12 6.078 -0.156 -0.094 -0.083 -0.083
## 97 DECO =~ C_REP3 5.997 -0.036 -0.045 -0.080 -0.080
## 98 AFCOM =~ Im12 5.990 -0.079 -0.090 -0.079 -0.079
## 99 BRAND =~ C_CR4 5.990 0.125 0.151 0.075 0.075
## 100 Im20 ~~ Im21 5.968 0.142 0.142 0.210 0.210
## 101 CHOICE =~ Im5 5.888 0.085 0.111 0.083 0.083
## 102 Im3 ~~ Im1 5.882 -0.036 -0.036 -0.282 -0.282
## 103 FRENCH =~ Im16 5.821 -0.123 -0.121 -0.100 -0.100
## 104 FOOD =~ C_REP1 5.726 0.065 0.053 0.072 0.072
## 105 DECO =~ Im20 5.672 -0.100 -0.124 -0.083 -0.083
## 106 BRAND =~ Im22 5.632 0.110 0.133 0.087 0.087
## 107 BRAND =~ C_REP3 5.604 -0.037 -0.044 -0.079 -0.079
## 108 FOOD =~ COM_A3 5.586 0.144 0.118 0.072 0.072
## 109 Im13 ~~ Im2 5.468 -0.048 -0.048 -0.138 -0.138
## 110 BRAND =~ Im7 5.379 -0.092 -0.111 -0.092 -0.092
## 111 DECO =~ Im17 5.370 -0.101 -0.125 -0.100 -0.100
## 112 DECO =~ Im18 5.370 0.100 0.124 0.089 0.089
## 113 Im3 ~~ Im22 5.361 0.052 0.052 0.154 0.154
## 114 ATMOS =~ Im4 5.339 -0.060 -0.075 -0.055 -0.055
## 115 PROF =~ Im12 5.308 -0.135 -0.125 -0.110 -0.110
## 116 Im3 ~~ Im5 5.278 -0.077 -0.077 -0.190 -0.190
## 117 FOOD =~ Im13 5.271 -0.128 -0.105 -0.087 -0.087
## 118 Im10 ~~ Im13 5.270 -0.032 -0.032 -0.157 -0.157
## 119 PROF =~ C_CR1 5.246 -0.154 -0.142 -0.072 -0.072
## 120 FOOD =~ Im7 5.241 0.298 0.244 0.201 0.201
## 121 Im10 ~~ Im7 5.217 0.034 0.034 0.280 0.280
## 122 Im20 ~~ Im17 5.189 -0.061 -0.061 -0.243 -0.243
## 123 CHOICE =~ COM_A3 5.126 0.085 0.111 0.068 0.068
## 124 SAT_1 ~~ SAT_3 5.057 0.089 0.089 0.199 0.199
## 125 Im4 ~~ C_CR1 5.037 -0.067 -0.067 -0.196 -0.196
## 126 DECO =~ Im7 5.030 -0.088 -0.109 -0.090 -0.090
## 127 FRENCH =~ Im22 5.003 0.113 0.111 0.072 0.072
## 128 PROF =~ C_CR4 4.996 0.157 0.145 0.072 0.072
## 129 Im3 ~~ Im4 4.983 0.162 0.162 1.057 1.057
## 130 Im22 ~~ Im1 4.882 0.055 0.055 0.278 0.278
## 131 SAT_2 ~~ SAT_3 4.881 -0.083 -0.083 -0.164 -0.164
## 132 FRENCH ~ SAT 4.825 0.141 0.127 0.127 0.127
## 133 FRENCH ~~ SAT 4.825 0.065 0.098 0.098 0.098
## 134 Im4 ~~ Im18 4.809 0.040 0.040 0.170 0.170
## 135 Im5 ~~ Im6 4.760 -0.066 -0.066 -0.109 -0.109
## 136 BRAND =~ Im6 4.759 0.073 0.089 0.074 0.074
## 137 BRAND =~ C_CR1 4.749 -0.106 -0.128 -0.065 -0.065
## 138 AFCOM =~ Im20 4.740 -0.109 -0.124 -0.083 -0.083
## 139 Im22 ~~ C_REP1 4.716 0.041 0.041 0.132 0.132
## 140 PROF =~ Im20 4.707 -0.136 -0.126 -0.084 -0.084
## 141 DECO =~ C_CR4 4.672 0.106 0.132 0.066 0.066
## 142 PROF =~ C_REP1 4.632 0.059 0.055 0.074 0.074
## 143 FOOD =~ Im5 4.601 0.119 0.098 0.073 0.073
## 144 CHOICE ~ AFCOM 4.576 0.113 0.098 0.098 0.098
## 145 CHOICE ~~ AFCOM 4.576 0.101 0.082 0.082 0.082
## 146 Im20 ~~ Im13 4.567 0.067 0.067 0.135 0.135
## 147 Im20 ~~ Im6 4.541 -0.066 -0.066 -0.119 -0.119
## 148 FOOD =~ C_CR1 4.532 -0.152 -0.124 -0.063 -0.063
## 149 Im11 ~~ Im6 4.496 -0.066 -0.066 -0.105 -0.105
## 150 Im13 ~~ Im16 4.455 -0.063 -0.063 -0.130 -0.130
## 151 PROF =~ SAT_2 4.427 0.126 0.117 0.116 0.116
## 152 Im22 ~~ Im11 4.415 0.079 0.079 0.122 0.122
## 153 Im22 ~~ C_REP2 4.415 -0.030 -0.030 -0.189 -0.189
## 154 DECO =~ Im22 4.373 0.089 0.111 0.072 0.072
## 155 AFCOM =~ Im5 4.321 0.080 0.091 0.068 0.068
## 156 SAT_1 ~~ C_REP2 4.321 -0.022 -0.022 -0.192 -0.192
## 157 Im1 ~~ C_REP3 4.313 -0.021 -0.021 -0.217 -0.217
## 158 Im11 ~~ C_REP1 4.307 0.040 0.040 0.104 0.104
## 159 DECO =~ Im6 4.301 0.069 0.085 0.071 0.071
## 160 COM_A2 ~~ COM_A3 4.298 -0.121 -0.121 -0.147 -0.147
## 161 C_REP2 ~~ C_CR4 4.290 -0.043 -0.043 -0.168 -0.168
## 162 PROF =~ SAT_1 4.288 -0.130 -0.120 -0.118 -0.118
## 163 SAT =~ C_CR1 4.283 -0.151 -0.132 -0.067 -0.067
## 164 SAT =~ C_REP2 4.273 -0.051 -0.045 -0.071 -0.071
## 165 Im22 ~~ SAT_3 4.258 -0.079 -0.079 -0.124 -0.124
## 166 DECO =~ COM_A2 4.246 -0.079 -0.098 -0.061 -0.061
## 167 Im20 ~~ COM_A4 4.188 0.091 0.091 0.121 0.121
## 168 Im19 ~~ C_REP2 4.183 0.024 0.024 0.180 0.180
## 169 Im11 ~~ Im1 4.064 -0.050 -0.050 -0.205 -0.205
## 170 RI =~ Im14 4.052 0.068 0.041 0.047 0.047
## 171 PROF =~ Im1 4.031 -0.187 -0.173 -0.130 -0.130
## 172 PROF =~ Im2 4.031 0.166 0.153 0.119 0.119
## 173 COM_A3 ~~ C_REP2 4.029 -0.033 -0.033 -0.160 -0.160
## 174 Im4 ~~ Im6 3.998 0.035 0.035 0.154 0.154
## 175 Im12 ~~ Im7 3.996 0.046 0.046 0.232 0.232
## 176 SAT_2 ~~ C_REP1 3.972 0.028 0.028 0.113 0.113
## 177 PRODQUAL =~ Im2 3.912 -0.122 -0.087 -0.068 -0.068
## 178 AFCOM ~~ COI 3.890 0.658 0.455 0.455 0.455
## 179 COI ~ FRENCH 3.888 -0.175 -0.101 -0.101 -0.101
## 180 Im14 ~~ COM_A2 3.862 -0.035 -0.035 -0.148 -0.148
## 181 Im14 ~~ C_CR1 3.853 -0.045 -0.045 -0.160 -0.160
## 182 COM_A1 ~~ COM_A3 3.823 -0.101 -0.101 -0.125 -0.125
## 183 Im1 ~~ SAT_1 3.797 0.036 0.036 0.253 0.253
## 184 COM_A1 ~~ SAT_3 3.791 0.077 0.077 0.102 0.102
## 185 FRENCH =~ Im20 3.778 -0.097 -0.095 -0.064 -0.064
## 186 COM_A1 ~~ SAT_1 3.778 -0.054 -0.054 -0.121 -0.121
## 187 RI =~ COM_A2 3.774 -0.179 -0.108 -0.067 -0.067
## 188 Im4 ~~ Im11 3.764 -0.042 -0.042 -0.143 -0.143
## 189 SAT_3 ~~ C_CR3 3.753 -0.110 -0.110 -0.109 -0.109
## 190 ATMOS =~ COM_A4 3.750 0.099 0.124 0.071 0.071
## 191 ATMOS =~ COM_A1 3.741 -0.086 -0.108 -0.076 -0.076
## 192 Im4 ~~ COM_A3 3.717 0.047 0.047 0.153 0.153
## 193 FRENCH =~ C_REP2 3.709 -0.034 -0.033 -0.052 -0.052
## 194 Im11 ~~ Im17 3.683 -0.051 -0.051 -0.181 -0.181
## 195 Im16 ~~ SAT_1 3.671 -0.051 -0.051 -0.127 -0.127
## 196 FRENCH =~ C_CR1 3.601 -0.115 -0.112 -0.057 -0.057
## 197 PRODQUAL =~ Im1 3.584 0.131 0.094 0.071 0.071
## 198 Im20 ~~ SAT_1 3.562 -0.052 -0.052 -0.125 -0.125
## 199 COM_A3 ~~ C_REP3 3.559 -0.034 -0.034 -0.100 -0.100
## 200 Im2 ~~ Im17 3.554 0.033 0.033 0.187 0.187
## 201 Im14 ~~ Im6 3.542 0.026 0.026 0.141 0.141
## 202 FRENCH =~ COM_A3 3.520 0.102 0.100 0.062 0.062
## 203 RI =~ Im5 3.506 0.135 0.081 0.061 0.061
## 204 SAT =~ Im13 3.474 0.089 0.078 0.065 0.065
## 205 COI =~ C_REP2 3.473 -0.020 -0.034 -0.055 -0.055
## 206 PROF ~ AFCOM 3.467 0.067 0.083 0.083 0.083
## 207 PROF ~~ AFCOM 3.467 0.060 0.069 0.069 0.069
## 208 SAT =~ COM_A4 3.420 0.110 0.096 0.055 0.055
## 209 COM_A4 ~~ C_CR4 3.405 0.118 0.118 0.108 0.108
## 210 Im20 ~~ C_REP2 3.390 0.027 0.027 0.152 0.152
## 211 Im2 ~~ SAT_2 3.373 0.034 0.034 0.105 0.105
## 212 PROF =~ COM_A2 3.372 -0.102 -0.095 -0.059 -0.059
## 213 Im10 ~~ C_CR1 3.319 0.043 0.043 0.124 0.124
## 214 PROF =~ Im13 3.314 0.112 0.104 0.086 0.086
## 215 SAT ~ ATMOS 3.308 0.068 0.097 0.097 0.097
## 216 SAT =~ COM_A2 3.302 -0.101 -0.089 -0.055 -0.055
## 217 Im13 ~~ C_REP1 3.286 -0.029 -0.029 -0.107 -0.107
## 218 PRODQUAL =~ C_REP3 3.259 -0.050 -0.036 -0.064 -0.064
## 219 Im18 ~~ Im6 3.255 0.047 0.047 0.095 0.095
## 220 COI ~ PROF 3.203 -0.266 -0.145 -0.145 -0.145
## 221 FOOD =~ C_CR4 3.179 0.134 0.110 0.055 0.055
## 222 FRENCH =~ Im11 3.164 0.084 0.082 0.071 0.071
## 223 Im3 ~~ Im17 3.147 0.028 0.028 0.191 0.191
## 224 Im13 ~~ COM_A2 3.097 -0.059 -0.059 -0.109 -0.109
## 225 Im20 ~~ Im22 3.083 0.137 0.137 0.235 0.235
## 226 SAT_1 ~~ C_CR4 3.070 0.069 0.069 0.114 0.114
## 227 Im22 ~~ Im12 3.052 -0.051 -0.051 -0.127 -0.127
## 228 ATMOS =~ C_REP2 3.030 -0.029 -0.037 -0.059 -0.059
## 229 Im18 ~~ COM_A1 3.019 -0.058 -0.058 -0.093 -0.093
## 230 PRODQUAL ~ RI 3.011 -0.156 -0.131 -0.131 -0.131
## 231 FRENCH ~ COI 3.008 -0.044 -0.076 -0.076 -0.076
## 232 COI =~ Im11 2.993 0.045 0.076 0.066 0.066
## 233 Im5 ~~ C_REP1 2.988 0.032 0.032 0.086 0.086
## 234 Im16 ~~ C_REP3 2.983 -0.026 -0.026 -0.092 -0.092
## 235 Im17 ~~ C_REP1 2.950 -0.023 -0.023 -0.169 -0.169
## 236 AFCOM =~ Im16 2.941 -0.067 -0.076 -0.063 -0.063
## 237 BRAND =~ SAT_2 2.896 0.051 0.062 0.062 0.062
## 238 ATMOS =~ C_CR1 2.880 -0.086 -0.108 -0.055 -0.055
## 239 Im1 ~~ Im17 2.877 -0.031 -0.031 -0.358 -0.358
## 240 Im22 ~~ COM_A1 2.820 -0.065 -0.065 -0.103 -0.103
## 241 Im3 ~~ Im2 2.806 0.025 0.025 0.096 0.096
## 242 AFCOM =~ C_CR4 2.789 0.103 0.118 0.059 0.059
## 243 Im13 ~~ C_REP2 2.779 0.020 0.020 0.145 0.145
## 244 Im2 ~~ C_REP2 2.737 -0.016 -0.016 -0.127 -0.127
## 245 Im10 ~~ Im11 2.736 0.028 0.028 0.095 0.095
## 246 DECO =~ Im12 2.736 -0.058 -0.072 -0.063 -0.063
## 247 Im3 ~~ COM_A4 2.696 0.043 0.043 0.099 0.099
## 248 COI =~ Im16 2.696 -0.040 -0.068 -0.057 -0.057
## 249 RI =~ Im16 2.688 -0.124 -0.075 -0.062 -0.062
## 250 Im14 ~~ SAT_2 2.684 0.020 0.020 0.128 0.128
## 251 Im5 ~~ Im1 2.660 0.039 0.039 0.166 0.166
## 252 AFCOM =~ SAT_1 2.646 0.046 0.052 0.051 0.051
## 253 Im14 ~~ Im7 2.640 -0.024 -0.024 -0.245 -0.245
## 254 COM_A4 ~~ C_REP1 2.638 0.036 0.036 0.090 0.090
## 255 Im11 ~~ SAT_1 2.625 0.044 0.044 0.095 0.095
## 256 ATMOS =~ Im13 2.614 0.059 0.074 0.061 0.061
## 257 FRENCH =~ C_CR4 2.595 0.103 0.100 0.050 0.050
## 258 SAT =~ COM_A1 2.582 0.085 0.074 0.052 0.052
## 259 Im7 ~~ C_REP2 2.567 -0.018 -0.018 -0.224 -0.224
## 260 Im22 ~~ SAT_1 2.556 0.043 0.043 0.115 0.115
## 261 Im12 ~~ SAT_3 2.547 0.047 0.047 0.098 0.098
## 262 FRENCH =~ Im1 2.545 -0.056 -0.054 -0.041 -0.041
## 263 COM_A3 ~~ SAT_1 2.540 0.049 0.049 0.102 0.102
## 264 SAT =~ Im4 2.533 -0.054 -0.048 -0.035 -0.035
## 265 Im20 ~~ COM_A2 2.529 -0.066 -0.066 -0.093 -0.093
## 266 Im13 ~~ SAT_2 2.529 0.036 0.036 0.101 0.101
## 267 Im5 ~~ Im7 2.525 0.046 0.046 0.145 0.145
## 268 SAT =~ Im5 2.522 0.084 0.074 0.055 0.055
## 269 CHOICE =~ Im14 2.514 0.027 0.035 0.040 0.040
## 270 CHOICE =~ Im10 2.514 -0.026 -0.034 -0.039 -0.039
## 271 COM_A1 ~~ C_REP2 2.496 0.023 0.023 0.123 0.123
## 272 Im12 ~~ Im6 2.490 -0.037 -0.037 -0.097 -0.097
## 273 Im5 ~~ Im14 2.480 0.025 0.025 0.108 0.108
## 274 Im21 ~~ C_CR4 2.464 0.087 0.087 0.087 0.087
## 275 Im4 ~~ Im22 2.450 -0.034 -0.034 -0.141 -0.141
## 276 Im11 ~~ C_REP2 2.441 -0.022 -0.022 -0.114 -0.114
## 277 Im4 ~~ Im1 2.433 0.022 0.022 0.248 0.248
## 278 Im3 ~~ Im11 2.401 0.035 0.035 0.084 0.084
## 279 Im5 ~~ COM_A2 2.368 0.062 0.062 0.080 0.080
## 280 CHOICE =~ C_CR4 2.359 0.072 0.094 0.047 0.047
## 281 Im3 ~~ C_CR1 2.343 0.048 0.048 0.099 0.099
## 282 COI =~ Im2 2.339 0.026 0.044 0.034 0.034
## 283 PRODQUAL =~ SAT_2 2.298 0.078 0.056 0.056 0.056
## 284 Im16 ~~ C_CR4 2.283 -0.079 -0.079 -0.086 -0.086
## 285 SAT ~ Im9 2.270 0.038 0.044 0.059 0.044
## 286 COM_A2 ~~ COM_A4 2.260 -0.096 -0.096 -0.117 -0.117
## 287 COM_A2 ~~ SAT_2 2.250 -0.045 -0.045 -0.089 -0.089
## 288 Im22 ~~ Im2 2.244 -0.037 -0.037 -0.092 -0.092
## 289 Im2 ~~ Im16 2.242 0.036 0.036 0.082 0.082
## 290 FOOD =~ SAT_2 2.242 0.062 0.051 0.051 0.051
## 291 SAT ~~ COI 2.241 0.169 0.164 0.164 0.164
## 292 SAT =~ Im20 2.225 -0.083 -0.073 -0.049 -0.049
## 293 Im3 ~~ Im20 2.210 -0.034 -0.034 -0.090 -0.090
## 294 FOOD =~ Im1 2.173 -0.064 -0.053 -0.039 -0.039
## 295 Im11 ~~ Im2 2.154 0.037 0.037 0.073 0.073
## 296 Im12 ~~ Im16 2.145 0.041 0.041 0.095 0.095
## 297 Im20 ~~ Im1 2.139 -0.037 -0.037 -0.168 -0.168
## 298 C_REP3 ~~ C_CR3 2.121 -0.034 -0.034 -0.081 -0.081
## 299 Im19 ~~ COM_A1 2.114 0.046 0.046 0.088 0.088
## 300 PROF =~ Im4 2.095 -0.072 -0.067 -0.049 -0.049
## 301 AFCOM =~ Im2 2.064 0.039 0.044 0.034 0.034
## 302 FOOD ~~ SAT 2.058 0.033 0.060 0.060 0.060
## 303 COI =~ Im13 2.046 -0.032 -0.054 -0.044 -0.044
## 304 COM_A1 ~~ C_CR3 2.034 0.082 0.082 0.082 0.082
## 305 Im2 ~~ C_CR1 2.023 0.049 0.049 0.085 0.085
## 306 COM_A2 ~~ SAT_3 2.020 0.059 0.059 0.077 0.077
## 307 CHOICE =~ Im21 2.005 0.053 0.069 0.051 0.051
## 308 Im10 ~~ Im12 1.994 0.019 0.019 0.101 0.101
## 309 Im2 ~~ C_REP1 1.980 0.018 0.018 0.074 0.074
## 310 Im5 ~~ SAT_2 1.972 0.038 0.038 0.076 0.076
## 311 SAT_2 ~~ C_CR3 1.967 0.058 0.058 0.086 0.086
## 312 Im7 ~~ COM_A1 1.946 -0.043 -0.043 -0.136 -0.136
## 313 FRENCH =~ Im5 1.933 0.063 0.062 0.046 0.046
## 314 Im21 ~~ C_CR3 1.933 -0.078 -0.078 -0.080 -0.080
## 315 Im14 ~~ C_REP3 1.929 0.010 0.010 0.099 0.099
## 316 PRODQUAL ~~ COI 1.928 0.112 0.102 0.102 0.102
## 317 Im14 ~~ Im12 1.922 -0.018 -0.018 -0.120 -0.120
## 318 Im3 ~~ Im14 1.910 -0.014 -0.014 -0.109 -0.109
## 319 PRODQUAL =~ Im16 1.902 -0.117 -0.084 -0.070 -0.070
## 320 RI =~ Im11 1.898 0.106 0.064 0.056 0.056
## 321 CHOICE =~ Im22 1.887 0.055 0.071 0.047 0.047
## 322 Im14 ~~ Im2 1.883 0.015 0.015 0.099 0.099
## 323 Im18 ~~ C_REP1 1.876 0.022 0.022 0.072 0.072
## 324 Im22 ~~ Im13 1.874 -0.042 -0.042 -0.094 -0.094
## 325 SAT_1 ~~ C_CR1 1.866 -0.051 -0.051 -0.097 -0.097
## 326 RI =~ SAT_1 1.848 -0.086 -0.052 -0.051 -0.051
## 327 ATMOS =~ COM_A2 1.837 -0.065 -0.081 -0.050 -0.050
## 328 BRAND =~ C_REP1 1.829 0.026 0.031 0.042 0.042
## 329 Im14 ~~ COM_A3 1.826 0.025 0.025 0.100 0.100
## 330 ATMOS ~~ COI 1.805 0.236 0.123 0.123 0.123
## 331 Im13 ~~ SAT_3 1.799 -0.042 -0.042 -0.078 -0.078
## 332 PRODQUAL =~ Im4 1.799 -0.061 -0.044 -0.032 -0.032
## 333 FRENCH =~ COM_A2 1.788 -0.070 -0.068 -0.043 -0.043
## 334 AFCOM =~ Im7 1.754 -0.056 -0.064 -0.053 -0.053
## 335 RI =~ Im7 1.748 -0.082 -0.050 -0.041 -0.041
## 336 COM_A1 ~~ SAT_2 1.742 0.038 0.038 0.075 0.075
## 337 RI =~ Im10 1.736 -0.045 -0.027 -0.031 -0.031
## 338 DECO =~ Im13 1.692 0.048 0.059 0.049 0.049
## 339 Im3 ~~ Im12 1.685 -0.022 -0.022 -0.087 -0.087
## 340 Im20 ~~ COM_A3 1.685 -0.056 -0.056 -0.075 -0.075
## 341 PRODQUAL =~ Im7 1.680 0.091 0.065 0.054 0.054
## 342 PRODQUAL =~ Im6 1.680 -0.077 -0.055 -0.046 -0.046
## 343 Im12 ~~ COM_A4 1.668 -0.043 -0.043 -0.085 -0.085
## 344 Im5 ~~ Im16 1.661 -0.045 -0.045 -0.067 -0.067
## 345 BRAND =~ Im3 1.644 0.034 0.042 0.031 0.031
## 346 C_REP3 ~~ C_CR4 1.628 0.029 0.029 0.069 0.069
## 347 Im3 ~~ COM_A3 1.620 -0.033 -0.033 -0.075 -0.075
## 348 Im20 ~~ COM_A1 1.613 -0.050 -0.050 -0.072 -0.072
## 349 Im22 ~~ SAT_2 1.602 -0.035 -0.035 -0.083 -0.083
## 350 ATMOS ~ SAT 1.592 0.107 0.075 0.075 0.075
## 351 ATMOS ~~ SAT 1.592 0.049 0.058 0.058 0.058
## 352 FRENCH =~ Im2 1.589 0.039 0.038 0.030 0.030
## 353 FOOD =~ Im16 1.577 -0.084 -0.069 -0.057 -0.057
## 354 CHOICE =~ Im19 1.566 -0.065 -0.084 -0.074 -0.074
## 355 CHOICE =~ Im16 1.566 0.062 0.081 0.067 0.067
## 356 Im7 ~~ COM_A2 1.550 -0.040 -0.040 -0.125 -0.125
## 357 ATMOS =~ SAT_2 1.546 0.035 0.044 0.044 0.044
## 358 PRODQUAL =~ Im22 1.545 -0.094 -0.067 -0.044 -0.044
## 359 Im12 ~~ Im13 1.519 0.089 0.089 0.260 0.260
## 360 Im7 ~~ SAT_3 1.514 0.037 0.037 0.117 0.117
## 361 SAT =~ Im19 1.509 -0.094 -0.083 -0.073 -0.073
## 362 Im13 ~~ Im18 1.499 -0.033 -0.033 -0.073 -0.073
## 363 Im19 ~~ Im17 1.476 0.028 0.028 0.148 0.148
## 364 FOOD =~ Im2 1.469 0.047 0.038 0.030 0.030
## 365 Im2 ~~ Im18 1.449 -0.026 -0.026 -0.063 -0.063
## 366 SAT =~ Im18 1.439 -0.063 -0.056 -0.040 -0.040
## 367 Im3 ~~ Im18 1.436 -0.023 -0.023 -0.069 -0.069
## 368 PRODQUAL =~ C_REP2 1.435 0.034 0.024 0.039 0.039
## 369 PRODQUAL =~ Im18 1.434 -0.107 -0.077 -0.055 -0.055
## 370 PRODQUAL =~ Im17 1.434 0.108 0.077 0.062 0.062
## 371 Im21 ~~ Im18 1.421 -0.038 -0.038 -0.063 -0.063
## 372 COI =~ Im1 1.418 -0.020 -0.034 -0.026 -0.026
## 373 Im17 ~~ COM_A1 1.411 0.032 0.032 0.118 0.118
## 374 ATMOS =~ Im17 1.403 -0.053 -0.067 -0.053 -0.053
## 375 ATMOS =~ Im18 1.403 0.053 0.066 0.047 0.047
## 376 Im10 ~~ Im17 1.392 -0.014 -0.014 -0.135 -0.135
## 377 ATMOS =~ COM_A3 1.392 0.058 0.073 0.045 0.045
## 378 PROF =~ Im5 1.388 0.080 0.074 0.055 0.055
## 379 Im14 ~~ C_CR4 1.386 0.028 0.028 0.089 0.089
## 380 FRENCH ~~ COI 1.385 -0.073 -0.049 -0.049 -0.049
## 381 Im6 ~~ Im7 1.381 0.423 0.423 1.688 1.688
## 382 FRENCH ~~ AFCOM 1.380 -0.085 -0.092 -0.092 -0.092
## 383 FRENCH ~ AFCOM 1.380 -0.095 -0.110 -0.110 -0.110
## 384 Im18 ~~ Im7 1.376 -0.029 -0.029 -0.113 -0.113
## 385 Im2 ~~ COM_A3 1.372 0.033 0.033 0.063 0.063
## 386 SAT =~ Im17 1.358 0.053 0.046 0.037 0.037
## 387 Im22 ~~ Im19 1.356 -0.036 -0.036 -0.083 -0.083
## 388 ATMOS =~ Im3 1.352 0.030 0.037 0.028 0.028
## 389 RI =~ Im4 1.351 -0.051 -0.031 -0.023 -0.023
## 390 COI =~ Im4 1.345 -0.017 -0.029 -0.021 -0.021
## 391 Im12 ~~ COM_A3 1.343 -0.038 -0.038 -0.074 -0.074
## 392 PROF =~ Im7 1.333 -0.073 -0.067 -0.055 -0.055
## 393 Im2 ~~ SAT_1 1.326 -0.021 -0.021 -0.072 -0.072
## 394 SAT =~ Im11 1.324 0.063 0.056 0.048 0.048
## 395 BRAND =~ Im16 1.322 -0.061 -0.073 -0.061 -0.061
## 396 Im14 ~~ Im17 1.321 0.014 0.014 0.159 0.159
## 397 Im4 ~~ Im2 1.296 -0.016 -0.016 -0.088 -0.088
## 398 Im13 ~~ COM_A4 1.296 0.041 0.041 0.071 0.071
## 399 Im10 ~~ C_CR4 1.296 -0.028 -0.028 -0.072 -0.072
## 400 C_REP1 ~~ C_CR3 1.287 0.032 0.032 0.064 0.064
## 401 Im20 ~~ SAT_2 1.280 0.032 0.032 0.068 0.068
## 402 SAT =~ Im14 1.277 0.029 0.026 0.029 0.029
## 403 PRODQUAL =~ COM_A2 1.276 -0.080 -0.057 -0.035 -0.035
## 404 Im1 ~~ COM_A4 1.274 -0.032 -0.032 -0.127 -0.127
## 405 COM_A2 ~~ C_CR1 1.273 0.064 0.064 0.070 0.070
## 406 Im12 ~~ Im17 1.266 -0.024 -0.024 -0.137 -0.137
## 407 Im11 ~~ Im7 1.262 0.033 0.033 0.103 0.103
## 408 Im3 ~~ Im10 1.253 0.011 0.011 0.073 0.073
## 409 FRENCH =~ SAT_3 1.247 0.051 0.050 0.044 0.044
## 410 FOOD =~ C_REP2 1.245 -0.023 -0.019 -0.030 -0.030
## 411 Im2 ~~ C_REP3 1.242 0.012 0.012 0.057 0.057
## 412 Im21 ~~ SAT_3 1.239 0.043 0.043 0.058 0.058
## 413 Im10 ~~ SAT_2 1.232 -0.014 -0.014 -0.072 -0.072
## 414 AFCOM ~ DECO 1.194 0.051 0.056 0.056 0.056
## 415 Im10 ~~ COM_A4 1.184 -0.021 -0.021 -0.069 -0.069
## 416 Im20 ~~ Im18 1.184 0.035 0.035 0.061 0.061
## 417 PRODQUAL =~ Im20 1.181 0.081 0.058 0.039 0.039
## 418 COM_A1 ~~ C_REP3 1.181 0.018 0.018 0.057 0.057
## 419 COM_A4 ~~ SAT_3 1.181 -0.048 -0.048 -0.059 -0.059
## 420 Im12 ~~ C_REP1 1.173 -0.016 -0.016 -0.067 -0.067
## 421 Im12 ~~ C_CR1 1.170 -0.043 -0.043 -0.076 -0.076
## 422 FRENCH =~ COM_A1 1.168 -0.053 -0.052 -0.036 -0.036
## 423 AFCOM =~ C_CR1 1.148 -0.064 -0.073 -0.037 -0.037
## 424 Im13 ~~ Im19 1.145 0.028 0.028 0.074 0.074
## 425 Im12 ~~ C_CR4 1.133 0.045 0.045 0.069 0.069
## 426 FRENCH =~ SAT_1 1.128 0.035 0.034 0.034 0.034
## 427 COI ~ DECO 1.125 -0.081 -0.059 -0.059 -0.059
## 428 Im4 ~~ Im7 1.121 -0.018 -0.018 -0.152 -0.152
## 429 ATMOS =~ C_CR3 1.117 -0.057 -0.071 -0.034 -0.034
## 430 Im6 ~~ C_REP2 1.115 0.012 0.012 0.081 0.081
## 431 Im5 ~~ Im19 1.102 -0.032 -0.032 -0.060 -0.060
## 432 Im14 ~~ Im13 1.102 0.015 0.015 0.087 0.087
## 433 COM_A1 ~~ C_CR1 1.102 -0.057 -0.057 -0.063 -0.063
## 434 Im12 ~~ SAT_2 1.084 -0.022 -0.022 -0.070 -0.070
## 435 Im21 ~~ Im11 1.082 -0.040 -0.040 -0.052 -0.052
## 436 AFCOM =~ SAT_3 1.080 0.041 0.046 0.041 0.041
## 437 COM_A3 ~~ SAT_2 1.076 0.033 0.033 0.061 0.061
## 438 ATMOS =~ Im2 1.059 -0.033 -0.041 -0.032 -0.032
## 439 BRAND =~ Im1 1.056 -0.044 -0.054 -0.040 -0.040
## 440 Im19 ~~ SAT_3 1.052 -0.033 -0.033 -0.062 -0.062
## 441 Im12 ~~ C_CR3 1.045 0.044 0.044 0.069 0.069
## 442 Im1 ~~ Im18 1.026 0.021 0.021 0.109 0.109
## 443 Im4 ~~ Im12 1.025 0.017 0.017 0.093 0.093
## 444 Im6 ~~ COM_A1 1.016 0.032 0.032 0.053 0.053
## 445 FOOD ~~ RI 1.014 0.015 0.038 0.038 0.038
## 446 Im19 ~~ Im18 1.012 -0.027 -0.027 -0.062 -0.062
## 447 Im6 ~~ SAT_1 1.004 0.022 0.022 0.062 0.062
## 448 COM_A4 ~~ C_CR3 1.003 -0.065 -0.065 -0.060 -0.060
## 449 Im18 ~~ COM_A2 0.991 0.035 0.035 0.055 0.055
## 450 Im7 ~~ COM_A4 0.991 0.034 0.034 0.102 0.102
## 451 Im4 ~~ COM_A4 0.990 -0.025 -0.025 -0.081 -0.081
## 452 Im18 ~~ C_REP3 0.977 -0.013 -0.013 -0.051 -0.051
## 453 FRENCH =~ Im13 0.975 -0.041 -0.040 -0.034 -0.034
## 454 Im1 ~~ COM_A2 0.975 0.026 0.026 0.110 0.110
## 455 BRAND =~ Im14 0.971 0.019 0.023 0.026 0.026
## 456 BRAND =~ Im10 0.971 -0.018 -0.022 -0.025 -0.025
## 457 Im3 ~~ SAT_1 0.968 0.016 0.016 0.066 0.066
## 458 Im16 ~~ Im7 0.965 -0.028 -0.028 -0.100 -0.100
## 459 SAT =~ Im1 0.958 -0.054 -0.048 -0.036 -0.036
## 460 Im17 ~~ COM_A4 0.947 -0.030 -0.030 -0.101 -0.101
## 461 PRODQUAL =~ COM_A3 0.944 0.071 0.051 0.031 0.031
## 462 COI =~ COM_A1 0.944 -0.028 -0.048 -0.034 -0.034
## 463 Im5 ~~ Im2 0.941 -0.024 -0.024 -0.049 -0.049
## 464 PROF =~ COM_A1 0.925 0.051 0.047 0.033 0.033
## 465 Im1 ~~ C_REP2 0.924 0.009 0.009 0.150 0.150
## 466 COM_A4 ~~ C_REP3 0.922 -0.017 -0.017 -0.052 -0.052
## 467 BRAND =~ Im11 0.921 -0.043 -0.052 -0.046 -0.046
## 468 Im11 ~~ COM_A3 0.908 0.041 0.041 0.049 0.049
## 469 AFCOM =~ Im21 0.901 0.045 0.052 0.038 0.038
## 470 Im22 ~~ Im7 0.899 0.028 0.028 0.108 0.108
## 471 FRENCH =~ COM_A4 0.898 0.053 0.052 0.030 0.030
## 472 FRENCH =~ C_CR3 0.897 -0.061 -0.060 -0.029 -0.029
## 473 Im13 ~~ Im6 0.894 0.024 0.024 0.056 0.056
## 474 Im1 ~~ COM_A1 0.890 0.024 0.024 0.101 0.101
## 475 Im12 ~~ COM_A2 0.889 0.030 0.030 0.061 0.061
## 476 BRAND =~ Im2 0.885 0.036 0.044 0.034 0.034
## 477 CHOICE =~ C_CR1 0.885 -0.042 -0.055 -0.028 -0.028
## 478 Im11 ~~ Im18 0.883 0.030 0.030 0.047 0.047
## 479 BRAND =~ COM_A4 0.882 -0.040 -0.049 -0.028 -0.028
## 480 Im12 ~~ SAT_1 0.871 -0.019 -0.019 -0.068 -0.068
## 481 Im13 ~~ Im7 0.856 -0.023 -0.023 -0.102 -0.102
## 482 Im4 ~~ C_CR3 0.851 0.029 0.029 0.077 0.077
## 483 AFCOM =~ Im4 0.842 -0.021 -0.024 -0.018 -0.018
## 484 COM_A4 ~~ C_REP2 0.841 -0.015 -0.015 -0.075 -0.075
## 485 Im4 ~~ Im5 0.841 0.033 0.033 0.115 0.115
## 486 Im22 ~~ Im16 0.832 0.033 0.033 0.058 0.058
## 487 Im18 ~~ SAT_1 0.828 -0.021 -0.021 -0.057 -0.057
## 488 PROF =~ Im11 0.823 0.056 0.052 0.045 0.045
## 489 PRODQUAL =~ SAT_1 0.817 -0.046 -0.033 -0.033 -0.033
## 490 SAT =~ Im2 0.812 0.045 0.039 0.031 0.031
## 491 Im20 ~~ SAT_3 0.812 0.035 0.035 0.050 0.050
## 492 FOOD =~ Im20 0.809 -0.052 -0.042 -0.028 -0.028
## 493 Im22 ~~ Im18 0.802 0.029 0.029 0.055 0.055
## 494 CHOICE =~ COM_A1 0.801 0.031 0.040 0.028 0.028
## 495 RI ~ CHOICE 0.797 -0.021 -0.046 -0.046 -0.046
## 496 Im22 ~~ COM_A3 0.797 0.038 0.038 0.056 0.056
## 497 Im16 ~~ C_CR1 0.792 0.044 0.044 0.055 0.055
## 498 Im17 ~~ COM_A3 0.787 0.027 0.027 0.090 0.090
## 499 Im17 ~~ C_REP2 0.780 0.009 0.009 0.127 0.127
## 500 Im14 ~~ Im21 0.773 0.015 0.015 0.064 0.064
## 501 PRODQUAL =~ Im19 0.770 0.074 0.053 0.047 0.047
## 502 PROF =~ Im22 0.768 0.056 0.052 0.034 0.034
## 503 Im3 ~~ Im19 0.764 0.016 0.016 0.058 0.058
## 504 Im7 ~~ COM_A3 0.762 0.029 0.029 0.087 0.087
## 505 Im20 ~~ Im7 0.758 0.026 0.026 0.090 0.090
## 506 Im5 ~~ C_REP2 0.753 -0.012 -0.012 -0.063 -0.063
## 507 SAT =~ Im21 0.751 0.047 0.041 0.030 0.030
## 508 Im20 ~~ Im19 0.750 0.027 0.027 0.056 0.056
## 509 Im5 ~~ Im11 0.740 0.032 0.032 0.041 0.041
## 510 BRAND =~ COM_A2 0.738 -0.034 -0.042 -0.026 -0.026
## 511 Im13 ~~ COM_A3 0.737 -0.030 -0.030 -0.052 -0.052
## 512 COI =~ C_REP3 0.735 -0.009 -0.016 -0.028 -0.028
## 513 Im16 ~~ COM_A4 0.735 -0.036 -0.036 -0.049 -0.049
## 514 Im11 ~~ C_CR4 0.729 0.047 0.047 0.045 0.045
## 515 SAT =~ Im22 0.727 -0.047 -0.041 -0.027 -0.027
## 516 Im19 ~~ SAT_1 0.727 -0.020 -0.020 -0.064 -0.064
## 517 Im11 ~~ COM_A2 0.725 0.035 0.035 0.044 0.044
## 518 Im5 ~~ C_CR4 0.714 0.046 0.046 0.044 0.044
## 519 COI =~ Im5 0.713 0.021 0.036 0.027 0.027
## 520 AFCOM =~ Im6 0.710 0.031 0.036 0.030 0.030
## 521 Im1 ~~ COM_A3 0.709 -0.024 -0.024 -0.092 -0.092
## 522 COI =~ Im3 0.698 0.013 0.022 0.016 0.016
## 523 SAT_3 ~~ C_REP3 0.697 0.013 0.013 0.043 0.043
## 524 Im6 ~~ C_CR4 0.693 -0.037 -0.037 -0.046 -0.046
## 525 Im9 ~ COI 0.693 0.031 0.052 0.038 0.038
## 526 Im19 ~~ SAT_2 0.691 0.020 0.020 0.056 0.056
## 527 Im10 ~~ Im18 0.691 0.012 0.012 0.050 0.050
## 528 PROF =~ Im18 0.687 -0.073 -0.067 -0.048 -0.048
## 529 PROF =~ Im17 0.687 0.073 0.068 0.054 0.054
## 530 Im22 ~~ Im6 0.686 0.025 0.025 0.050 0.050
## 531 Im21 ~~ COM_A4 0.686 -0.036 -0.036 -0.046 -0.046
## 532 COM_A3 ~~ SAT_3 0.682 -0.036 -0.036 -0.044 -0.044
## 533 SAT_3 ~~ C_CR1 0.679 0.044 0.044 0.048 0.048
## 534 Im13 ~~ C_CR3 0.674 -0.038 -0.038 -0.053 -0.053
## 535 Im22 ~~ COM_A4 0.671 0.036 0.036 0.053 0.053
## 536 Im6 ~~ COM_A3 0.669 -0.029 -0.029 -0.044 -0.044
## 537 ATMOS =~ Im1 0.669 0.030 0.037 0.028 0.028
## 538 Im10 ~~ C_REP3 0.665 -0.006 -0.006 -0.048 -0.048
## 539 Im21 ~~ C_REP1 0.665 -0.016 -0.016 -0.043 -0.043
## 540 COI ~ RI 0.661 1.089 0.388 0.388 0.388
## 541 COI ~ Im9 0.661 -0.044 -0.026 -0.035 -0.026
## 542 Im10 ~~ COM_A1 0.654 -0.014 -0.014 -0.049 -0.049
## 543 RI =~ Im13 0.651 0.054 0.033 0.027 0.027
## 544 CHOICE =~ SAT_2 0.650 -0.025 -0.033 -0.033 -0.033
## 545 DECO =~ SAT_2 0.642 0.024 0.029 0.029 0.029
## 546 Im4 ~~ COM_A2 0.641 -0.019 -0.019 -0.064 -0.064
## 547 Im22 ~~ Im17 0.640 0.021 0.021 0.094 0.094
## 548 Im14 ~~ Im18 0.639 -0.011 -0.011 -0.058 -0.058
## 549 PROF =~ Im3 0.639 0.039 0.036 0.027 0.027
## 550 SAT =~ Im16 0.635 -0.061 -0.054 -0.044 -0.044
## 551 SAT =~ C_CR3 0.631 -0.061 -0.054 -0.026 -0.026
## 552 Im10 ~~ Im2 0.630 -0.009 -0.009 -0.048 -0.048
## 553 Im14 ~~ SAT_1 0.629 -0.009 -0.009 -0.068 -0.068
## 554 CHOICE ~ COI 0.627 0.024 0.032 0.032 0.032
## 555 CHOICE =~ SAT_1 0.626 0.026 0.034 0.033 0.033
## 556 AFCOM =~ Im1 0.625 -0.022 -0.025 -0.019 -0.019
## 557 Im22 ~~ C_CR1 0.618 -0.041 -0.041 -0.054 -0.054
## 558 Im7 ~~ C_CR4 0.617 0.034 0.034 0.079 0.079
## 559 Im21 ~~ COM_A1 0.613 0.031 0.031 0.042 0.042
## 560 Im10 ~~ COM_A3 0.607 -0.015 -0.015 -0.048 -0.048
## 561 FRENCH ~ RI 0.603 -0.060 -0.037 -0.037 -0.037
## 562 Im7 ~~ C_REP1 0.600 0.012 0.012 0.074 0.074
## 563 CHOICE =~ C_REP2 0.588 -0.010 -0.013 -0.021 -0.021
## 564 Im4 ~~ Im16 0.575 0.016 0.016 0.062 0.062
## 565 CHOICE =~ Im3 0.569 -0.017 -0.022 -0.017 -0.017
## 566 COM_A2 ~~ C_CR4 0.567 -0.045 -0.045 -0.043 -0.043
## 567 COM_A1 ~~ C_REP1 0.562 -0.015 -0.015 -0.040 -0.040
## 568 FOOD =~ SAT_3 0.558 0.042 0.034 0.030 0.030
## 569 Im4 ~~ Im10 0.555 -0.007 -0.007 -0.066 -0.066
## 570 CHOICE ~~ RI 0.555 -0.018 -0.029 -0.029 -0.029
## 571 Im16 ~~ SAT_3 0.552 0.027 0.027 0.040 0.040
## 572 BRAND =~ SAT_3 0.544 -0.029 -0.035 -0.031 -0.031
## 573 Im21 ~~ SAT_2 0.540 -0.020 -0.020 -0.042 -0.042
## 574 ATMOS =~ Im19 0.534 -0.032 -0.041 -0.036 -0.036
## 575 Im11 ~~ COM_A1 0.533 -0.029 -0.029 -0.037 -0.037
## 576 Im16 ~~ COM_A3 0.529 0.030 0.030 0.041 0.041
## 577 COI =~ Im21 0.524 0.019 0.033 0.024 0.024
## 578 COM_A2 ~~ C_CR3 0.507 -0.043 -0.043 -0.042 -0.042
## 579 PRODQUAL =~ Im14 0.506 0.028 0.020 0.023 0.023
## 580 PRODQUAL =~ Im10 0.506 -0.028 -0.020 -0.022 -0.022
## 581 SAT_3 ~~ C_REP2 0.505 -0.010 -0.010 -0.054 -0.054
## 582 Im17 ~~ C_REP3 0.499 0.008 0.008 0.068 0.068
## 583 COM_A4 ~~ SAT_2 0.492 0.023 0.023 0.042 0.042
## 584 Im6 ~~ SAT_3 0.491 -0.022 -0.022 -0.036 -0.036
## 585 SAT_1 ~~ C_REP1 0.490 0.010 0.010 0.043 0.043
## 586 Im6 ~~ COM_A2 0.490 0.023 0.023 0.038 0.038
## 587 FOOD =~ C_CR3 0.487 -0.053 -0.043 -0.021 -0.021
## 588 Im21 ~~ Im17 0.486 0.018 0.018 0.070 0.070
## 589 PROF ~~ COI 0.483 -0.042 -0.030 -0.030 -0.030
## 590 Im22 ~~ COM_A2 0.482 0.028 0.028 0.044 0.044
## 591 Im7 ~~ C_REP3 0.479 0.008 0.008 0.065 0.065
## 592 Im16 ~~ SAT_2 0.478 0.019 0.019 0.041 0.041
## 593 Im2 ~~ COM_A1 0.478 -0.018 -0.018 -0.037 -0.037
## 594 Im10 ~~ SAT_3 0.477 0.012 0.012 0.041 0.041
## 595 Im14 ~~ Im20 0.474 -0.012 -0.012 -0.053 -0.053
## 596 Im7 ~~ SAT_2 0.473 -0.015 -0.015 -0.071 -0.071
## 597 Im7 ~~ C_CR1 0.472 -0.028 -0.028 -0.074 -0.074
## 598 RI =~ Im6 0.466 0.043 0.026 0.022 0.022
## 599 Im3 ~~ COM_A2 0.464 -0.017 -0.017 -0.041 -0.041
## 600 Im5 ~~ Im21 0.461 -0.025 -0.025 -0.034 -0.034
## 601 FOOD ~~ COI 0.453 -0.032 -0.025 -0.025 -0.025
## 602 SAT_1 ~~ C_CR3 0.452 -0.027 -0.027 -0.045 -0.045
## 603 SAT ~~ RI 0.452 0.024 0.073 0.073 0.073
## 604 SAT ~ PRODQUAL 0.448 0.046 0.038 0.038 0.038
## 605 Im3 ~~ C_CR4 0.447 -0.022 -0.022 -0.040 -0.040
## 606 COM_A1 ~~ C_CR4 0.443 -0.038 -0.038 -0.037 -0.037
## 607 Im19 ~~ Im7 0.442 0.017 0.017 0.078 0.078
## 608 Im20 ~~ C_REP3 0.442 -0.011 -0.011 -0.037 -0.037
## 609 Im10 ~~ Im20 0.441 0.011 0.011 0.043 0.043
## 610 RI =~ Im1 0.434 -0.035 -0.021 -0.016 -0.016
## 611 Im10 ~~ SAT_1 0.433 0.008 0.008 0.047 0.047
## 612 FOOD =~ COM_A2 0.433 -0.038 -0.031 -0.020 -0.020
## 613 AFCOM =~ Im14 0.433 0.012 0.014 0.016 0.016
## 614 RI =~ Im18 0.432 -0.045 -0.027 -0.019 -0.019
## 615 COI =~ Im12 0.429 0.014 0.023 0.020 0.020
## 616 FOOD =~ Im3 0.428 -0.023 -0.019 -0.014 -0.014
## 617 COI =~ COM_A3 0.427 -0.021 -0.036 -0.022 -0.022
## 618 Im5 ~~ Im22 0.421 0.024 0.024 0.038 0.038
## 619 Im5 ~~ Im17 0.417 0.017 0.017 0.060 0.060
## 620 Im10 ~~ C_CR3 0.414 -0.016 -0.016 -0.042 -0.042
## 621 Im12 ~~ Im2 0.412 -0.012 -0.012 -0.040 -0.040
## 622 Im20 ~~ Im2 0.409 -0.016 -0.016 -0.036 -0.036
## 623 Im4 ~~ C_REP3 0.407 -0.006 -0.006 -0.048 -0.048
## 624 C_REP3 ~~ C_CR1 0.407 0.014 0.014 0.037 0.037
## 625 Im12 ~~ C_REP2 0.404 0.007 0.007 0.058 0.058
## 626 PRODQUAL =~ COM_A1 0.401 0.042 0.030 0.021 0.021
## 627 Im10 ~~ Im19 0.401 -0.009 -0.009 -0.045 -0.045
## 628 DECO =~ SAT_1 0.401 -0.019 -0.024 -0.023 -0.023
## 629 FOOD =~ Im19 0.400 -0.042 -0.035 -0.030 -0.030
## 630 Im5 ~~ C_CR3 0.399 -0.034 -0.034 -0.034 -0.034
## 631 CHOICE =~ C_CR3 0.399 -0.030 -0.039 -0.019 -0.019
## 632 Im4 ~~ SAT_1 0.397 -0.010 -0.010 -0.058 -0.058
## 633 PROF =~ Im6 0.396 0.034 0.031 0.026 0.026
## 634 FRENCH =~ SAT_2 0.396 0.021 0.021 0.021 0.021
## 635 Im2 ~~ COM_A4 0.395 0.018 0.018 0.035 0.035
## 636 Im3 ~~ Im7 0.394 -0.011 -0.011 -0.066 -0.066
## 637 Im5 ~~ Im10 0.387 -0.010 -0.010 -0.036 -0.036
## 638 COM_A2 ~~ C_REP3 0.385 -0.011 -0.011 -0.033 -0.033
## 639 C_REP2 ~~ C_CR3 0.380 0.013 0.013 0.051 0.051
## 640 COI =~ Im7 0.379 -0.013 -0.022 -0.018 -0.018
## 641 BRAND =~ Im19 0.377 0.032 0.039 0.034 0.034
## 642 DECO =~ Im11 0.370 0.024 0.030 0.026 0.026
## 643 Im17 ~~ Im7 0.369 -0.013 -0.013 -0.117 -0.117
## 644 ATMOS ~ Im9 0.368 0.021 0.017 0.023 0.017
## 645 Im17 ~~ SAT_3 0.364 -0.016 -0.016 -0.059 -0.059
## 646 DECO =~ SAT_3 0.362 -0.023 -0.028 -0.025 -0.025
## 647 Im16 ~~ C_REP1 0.359 0.011 0.011 0.032 0.032
## 648 Im4 ~~ Im14 0.352 0.006 0.006 0.064 0.064
## 649 Im1 ~~ C_CR1 0.347 -0.020 -0.020 -0.071 -0.071
## 650 PROF =~ C_CR3 0.347 -0.042 -0.039 -0.019 -0.019
## 651 Im5 ~~ Im20 0.346 0.022 0.022 0.031 0.031
## 652 FRENCH =~ Im3 0.345 -0.017 -0.017 -0.012 -0.012
## 653 COM_A2 ~~ C_REP2 0.345 -0.009 -0.009 -0.047 -0.047
## 654 CHOICE =~ Im11 0.341 -0.022 -0.029 -0.025 -0.025
## 655 COI =~ Im14 0.339 -0.007 -0.011 -0.013 -0.013
## 656 Im19 ~~ COM_A2 0.338 -0.019 -0.019 -0.037 -0.037
## 657 SAT =~ Im6 0.337 0.026 0.023 0.019 0.019
## 658 AFCOM =~ Im13 0.334 -0.020 -0.023 -0.019 -0.019
## 659 Im17 ~~ SAT_1 0.332 0.011 0.011 0.067 0.067
## 660 BRAND =~ SAT_1 0.330 -0.017 -0.021 -0.020 -0.020
## 661 Im13 ~~ COM_A1 0.327 0.018 0.018 0.034 0.034
## 662 Im14 ~~ COM_A4 0.326 0.011 0.011 0.044 0.044
## 663 Im4 ~~ SAT_2 0.318 -0.009 -0.009 -0.047 -0.047
## 664 Im2 ~~ Im7 0.311 0.011 0.011 0.054 0.054
## 665 FOOD =~ COM_A1 0.310 -0.031 -0.025 -0.018 -0.018
## 666 Im16 ~~ C_CR3 0.293 -0.029 -0.029 -0.032 -0.032
## 667 Im17 ~~ C_CR1 0.290 -0.020 -0.020 -0.060 -0.060
## 668 PRODQUAL ~ COI 0.285 0.016 0.038 0.038 0.038
## 669 Im21 ~~ Im12 0.276 0.015 0.015 0.033 0.033
## 670 Im2 ~~ Im19 0.275 -0.011 -0.011 -0.032 -0.032
## 671 RI =~ Im20 0.273 0.043 0.026 0.018 0.018
## 672 CHOICE =~ Im6 0.271 -0.015 -0.019 -0.016 -0.016
## 673 Im22 ~~ C_CR3 0.267 0.029 0.029 0.034 0.034
## 674 Im21 ~~ C_CR1 0.262 0.027 0.027 0.031 0.031
## 675 Im18 ~~ C_REP2 0.262 -0.006 -0.006 -0.039 -0.039
## 676 Im20 ~~ Im12 0.262 0.015 0.015 0.034 0.034
## 677 COI =~ Im6 0.262 -0.011 -0.018 -0.015 -0.015
## 678 CHOICE =~ Im4 0.258 -0.012 -0.015 -0.011 -0.011
## 679 Im4 ~~ C_CR4 0.258 0.016 0.016 0.041 0.041
## 680 FRENCH =~ C_REP3 0.258 -0.010 -0.009 -0.017 -0.017
## 681 SAT =~ Im3 0.256 0.017 0.015 0.011 0.011
## 682 Im21 ~~ Im16 0.254 -0.018 -0.018 -0.028 -0.028
## 683 Im1 ~~ SAT_3 0.254 0.013 0.013 0.053 0.053
## 684 Im21 ~~ Im7 0.251 -0.015 -0.015 -0.049 -0.049
## 685 Im1 ~~ Im16 0.251 -0.012 -0.012 -0.057 -0.057
## 686 AFCOM =~ C_CR3 0.243 -0.031 -0.036 -0.017 -0.017
## 687 Im17 ~~ SAT_2 0.242 0.010 0.010 0.052 0.052
## 688 SAT_3 ~~ C_CR4 0.240 0.028 0.028 0.027 0.027
## 689 FOOD =~ Im21 0.237 0.027 0.022 0.016 0.016
## 690 FOOD ~~ AFCOM 0.235 0.014 0.018 0.018 0.018
## 691 Im20 ~~ C_REP1 0.232 -0.009 -0.009 -0.027 -0.027
## 692 ATMOS ~~ RI 0.230 0.027 0.043 0.043 0.043
## 693 Im11 ~~ SAT_2 0.228 -0.013 -0.013 -0.026 -0.026
## 694 Im19 ~~ COM_A4 0.226 -0.017 -0.017 -0.030 -0.030
## 695 Im21 ~~ Im2 0.226 0.012 0.012 0.025 0.025
## 696 CHOICE =~ Im18 0.225 -0.020 -0.025 -0.018 -0.018
## 697 CHOICE =~ Im17 0.225 0.020 0.026 0.020 0.020
## 698 SAT =~ C_REP3 0.224 -0.011 -0.010 -0.018 -0.018
## 699 Im17 ~~ COM_A2 0.222 -0.013 -0.013 -0.048 -0.048
## 700 COM_A3 ~~ C_CR3 0.221 0.030 0.030 0.028 0.028
## 701 RI =~ Im2 0.219 0.025 0.015 0.012 0.012
## 702 Im17 ~~ C_CR4 0.211 0.018 0.018 0.047 0.047
## 703 RI =~ COM_A3 0.207 0.044 0.026 0.016 0.016
## 704 AFCOM ~ Im9 0.207 0.015 0.013 0.018 0.013
## 705 CHOICE =~ COM_A4 0.207 -0.018 -0.023 -0.013 -0.013
## 706 RI =~ Im3 0.206 0.020 0.012 0.009 0.009
## 707 Im21 ~~ COM_A2 0.206 0.019 0.019 0.025 0.025
## 708 Im5 ~~ SAT_1 0.206 -0.012 -0.012 -0.027 -0.027
## 709 C_REP2 ~~ C_CR1 0.203 0.009 0.009 0.039 0.039
## 710 Im17 ~~ Im6 0.198 0.010 0.010 0.044 0.044
## 711 SAT_2 ~~ C_REP3 0.193 0.005 0.005 0.024 0.024
## 712 ATMOS =~ Im16 0.191 -0.020 -0.025 -0.020 -0.020
## 713 ATMOS =~ Im14 0.187 0.008 0.010 0.011 0.011
## 714 ATMOS =~ Im10 0.187 -0.008 -0.010 -0.011 -0.011
## 715 Im19 ~~ Im6 0.183 -0.011 -0.011 -0.026 -0.026
## 716 Im14 ~~ C_CR3 0.183 0.010 0.010 0.033 0.033
## 717 Im2 ~~ C_CR4 0.181 -0.016 -0.016 -0.023 -0.023
## 718 Im14 ~~ Im22 0.180 -0.007 -0.007 -0.036 -0.036
## 719 Im14 ~~ SAT_3 0.180 -0.007 -0.007 -0.030 -0.030
## 720 C_CR1 ~~ C_CR3 0.178 0.112 0.112 0.093 0.093
## 721 SAT =~ Im10 0.177 -0.011 -0.010 -0.011 -0.011
## 722 Im6 ~~ C_REP1 0.176 -0.007 -0.007 -0.022 -0.022
## 723 Im10 ~~ Im21 0.176 -0.007 -0.007 -0.025 -0.025
## 724 Im21 ~~ Im1 0.175 0.010 0.010 0.045 0.045
## 725 Im21 ~~ COM_A3 0.174 -0.018 -0.018 -0.023 -0.023
## 726 Im6 ~~ C_CR1 0.174 0.018 0.018 0.025 0.025
## 727 PROF ~ Im9 0.171 -0.009 -0.010 -0.014 -0.010
## 728 Im3 ~~ SAT_2 0.170 -0.007 -0.007 -0.025 -0.025
## 729 Im4 ~~ C_REP2 0.169 0.003 0.003 0.046 0.046
## 730 Im3 ~~ COM_A1 0.169 -0.010 -0.010 -0.024 -0.024
## 731 Im5 ~~ COM_A4 0.169 -0.018 -0.018 -0.022 -0.022
## 732 DECO =~ C_REP2 0.166 -0.006 -0.007 -0.011 -0.011
## 733 Im14 ~~ Im11 0.166 0.007 0.007 0.028 0.028
## 734 COM_A2 ~~ SAT_1 0.164 -0.012 -0.012 -0.026 -0.026
## 735 AFCOM =~ Im10 0.164 -0.007 -0.009 -0.010 -0.010
## 736 SAT_2 ~~ C_CR4 0.162 0.016 0.016 0.024 0.024
## 737 Im4 ~~ COM_A1 0.161 0.009 0.009 0.031 0.031
## 738 Im1 ~~ Im2 0.161 0.350 0.350 2.277 2.277
## 739 CHOICE ~ SAT 0.160 -0.102 -0.069 -0.069 -0.069
## 740 CHOICE ~~ SAT 0.160 -0.047 -0.053 -0.053 -0.053
## 741 Im12 ~~ C_REP3 0.159 -0.005 -0.005 -0.024 -0.024
## 742 PROF =~ SAT_3 0.158 -0.028 -0.026 -0.023 -0.023
## 743 Im20 ~~ Im11 0.157 0.015 0.015 0.021 0.021
## 744 Im14 ~~ Im1 0.157 -0.004 -0.004 -0.059 -0.059
## 745 Im19 ~~ COM_A3 0.155 -0.014 -0.014 -0.024 -0.024
## 746 Im19 ~~ C_REP3 0.153 0.005 0.005 0.023 0.023
## 747 Im17 ~~ C_CR3 0.153 0.015 0.015 0.042 0.042
## 748 Im1 ~~ Im6 0.151 -0.008 -0.008 -0.041 -0.041
## 749 Im5 ~~ COM_A1 0.150 -0.015 -0.015 -0.020 -0.020
## 750 COI =~ COM_A4 0.146 0.013 0.022 0.012 0.012
## 751 PROF ~~ RI 0.142 -0.007 -0.016 -0.016 -0.016
## 752 Im14 ~~ C_REP1 0.138 0.003 0.003 0.027 0.027
## 753 Im20 ~~ C_CR1 0.135 0.019 0.019 0.023 0.023
## 754 DECO ~~ COI 0.135 -0.026 -0.014 -0.014 -0.014
## 755 BRAND =~ C_REP2 0.133 0.005 0.007 0.010 0.010
## 756 FRENCH =~ Im18 0.131 0.015 0.015 0.011 0.011
## 757 FRENCH =~ Im17 0.131 -0.015 -0.015 -0.012 -0.012
## 758 FRENCH =~ Im21 0.127 -0.017 -0.017 -0.012 -0.012
## 759 Im16 ~~ Im18 0.127 -0.011 -0.011 -0.020 -0.020
## 760 PRODQUAL =~ COM_A4 0.127 -0.027 -0.019 -0.011 -0.011
## 761 Im3 ~~ C_REP1 0.127 0.004 0.004 0.020 0.020
## 762 Im12 ~~ COM_A1 0.127 0.011 0.011 0.022 0.022
## 763 Im16 ~~ COM_A1 0.126 -0.013 -0.013 -0.019 -0.019
## 764 AFCOM =~ Im18 0.125 -0.013 -0.014 -0.010 -0.010
## 765 Im3 ~~ C_REP3 0.123 0.003 0.003 0.020 0.020
## 766 Im13 ~~ SAT_1 0.122 -0.008 -0.008 -0.024 -0.024
## 767 Im7 ~~ C_CR3 0.122 -0.015 -0.015 -0.036 -0.036
## 768 COI =~ SAT_3 0.117 -0.009 -0.015 -0.014 -0.014
## 769 DECO =~ COM_A4 0.116 0.014 0.017 0.010 0.010
## 770 Im4 ~~ Im19 0.115 -0.006 -0.006 -0.031 -0.031
## 771 Im11 ~~ Im19 0.114 -0.010 -0.010 -0.019 -0.019
## 772 Im5 ~~ SAT_3 0.111 -0.013 -0.013 -0.016 -0.016
## 773 SAT_2 ~~ C_CR1 0.111 -0.013 -0.013 -0.021 -0.021
## 774 Im11 ~~ COM_A4 0.111 0.015 0.015 0.018 0.018
## 775 Im4 ~~ Im20 0.109 0.007 0.007 0.027 0.027
## 776 Im11 ~~ C_CR1 0.108 -0.017 -0.017 -0.019 -0.019
## 777 Im20 ~~ C_CR3 0.106 -0.018 -0.018 -0.020 -0.020
## 778 Im4 ~~ C_REP1 0.104 -0.004 -0.004 -0.025 -0.025
## 779 PROF ~ COI 0.104 0.008 0.014 0.014 0.014
## 780 COM_A3 ~~ C_CR1 0.104 -0.019 -0.019 -0.020 -0.020
## 781 FOOD =~ Im4 0.102 -0.012 -0.010 -0.007 -0.007
## 782 Im21 ~~ Im13 0.102 -0.010 -0.010 -0.019 -0.019
## 783 ATMOS =~ SAT_1 0.100 0.009 0.011 0.011 0.011
## 784 Im2 ~~ Im6 0.099 -0.006 -0.006 -0.016 -0.016
## 785 AFCOM =~ Im19 0.099 -0.011 -0.012 -0.011 -0.011
## 786 DECO ~~ RI 0.098 0.007 0.012 0.012 0.012
## 787 PRODQUAL ~ SAT 0.098 -0.015 -0.018 -0.018 -0.018
## 788 PRODQUAL ~~ SAT 0.098 -0.007 -0.014 -0.014 -0.014
## 789 Im18 ~~ C_CR1 0.097 0.014 0.014 0.019 0.019
## 790 Im6 ~~ C_REP3 0.095 -0.004 -0.004 -0.016 -0.016
## 791 DECO ~ COI 0.094 -0.009 -0.012 -0.012 -0.012
## 792 Im1 ~~ C_CR3 0.093 -0.011 -0.011 -0.035 -0.035
## 793 Im18 ~~ SAT_2 0.093 0.007 0.007 0.017 0.017
## 794 AFCOM =~ Im22 0.091 0.015 0.018 0.011 0.011
## 795 RI ~ PROF 0.090 -0.014 -0.021 -0.021 -0.021
## 796 DECO ~ AFCOM 0.087 -0.014 -0.013 -0.013 -0.013
## 797 DECO ~~ AFCOM 0.087 -0.013 -0.011 -0.011 -0.011
## 798 DECO =~ Im1 0.086 -0.010 -0.013 -0.010 -0.010
## 799 DECO =~ Im2 0.086 0.009 0.011 0.009 0.009
## 800 Im14 ~~ COM_A1 0.085 0.005 0.005 0.021 0.021
## 801 Im6 ~~ SAT_2 0.084 -0.007 -0.007 -0.016 -0.016
## 802 RI =~ C_CR1 0.084 -0.029 -0.018 -0.009 -0.009
## 803 FRENCH ~~ RI 0.083 -0.006 -0.012 -0.012 -0.012
## 804 Im3 ~~ C_REP2 0.079 -0.002 -0.002 -0.023 -0.023
## 805 Im10 ~~ C_REP1 0.078 0.002 0.002 0.017 0.017
## 806 FRENCH =~ Im14 0.077 0.011 0.011 0.013 0.013
## 807 FRENCH =~ Im10 0.077 -0.011 -0.011 -0.012 -0.012
## 808 DECO ~ Im9 0.075 0.008 0.007 0.009 0.007
## 809 COM_A2 ~~ C_REP1 0.075 0.006 0.006 0.015 0.015
## 810 Im3 ~~ Im13 0.073 0.005 0.005 0.017 0.017
## 811 Im10 ~~ C_REP2 0.071 -0.002 -0.002 -0.023 -0.023
## 812 BRAND ~~ COI 0.071 0.018 0.010 0.010 0.010
## 813 Im3 ~~ SAT_3 0.070 -0.006 -0.006 -0.015 -0.015
## 814 Im18 ~~ C_CR4 0.070 -0.012 -0.012 -0.015 -0.015
## 815 FOOD =~ SAT_1 0.068 -0.011 -0.009 -0.009 -0.009
## 816 PROF =~ Im21 0.067 0.016 0.014 0.010 0.010
## 817 Im5 ~~ Im18 0.066 0.008 0.008 0.013 0.013
## 818 COI ~ CHOICE 0.066 -0.020 -0.015 -0.015 -0.015
## 819 SAT_1 ~~ C_REP3 0.063 0.003 0.003 0.015 0.015
## 820 RI ~ FRENCH 0.063 0.007 0.011 0.011 0.011
## 821 AFCOM ~~ RI 0.063 -0.026 -0.057 -0.057 -0.057
## 822 C_REP1 ~~ C_CR4 0.061 -0.007 -0.007 -0.014 -0.014
## 823 FOOD =~ C_REP3 0.061 -0.005 -0.005 -0.008 -0.008
## 824 PRODQUAL =~ Im21 0.061 0.018 0.013 0.009 0.009
## 825 Im18 ~~ COM_A4 0.058 -0.009 -0.009 -0.013 -0.013
## 826 Im5 ~~ COM_A3 0.057 -0.010 -0.010 -0.012 -0.012
## 827 Im19 ~~ C_CR3 0.057 0.011 0.011 0.016 0.016
## 828 Im13 ~~ C_REP3 0.056 0.003 0.003 0.014 0.014
## 829 Im12 ~~ Im18 0.053 -0.006 -0.006 -0.015 -0.015
## 830 Im10 ~~ Im1 0.053 -0.003 -0.003 -0.028 -0.028
## 831 CHOICE =~ SAT_3 0.053 0.009 0.012 0.010 0.010
## 832 C_CR3 ~~ C_CR4 0.051 -0.054 -0.054 -0.039 -0.039
## 833 SAT_3 ~~ C_REP1 0.051 -0.004 -0.004 -0.012 -0.012
## 834 BRAND ~~ SAT 0.050 0.007 0.009 0.009 0.009
## 835 Im4 ~~ Im21 0.049 0.005 0.005 0.017 0.017
## 836 ATMOS =~ Im7 0.049 0.009 0.011 0.009 0.009
## 837 ATMOS =~ Im6 0.049 -0.008 -0.009 -0.008 -0.008
## 838 RI =~ COM_A4 0.048 0.022 0.013 0.007 0.007
## 839 Im18 ~~ C_CR3 0.047 -0.010 -0.010 -0.012 -0.012
## 840 Im11 ~~ Im16 0.047 -0.008 -0.008 -0.011 -0.011
## 841 RI ~ DECO 0.045 0.005 0.010 0.010 0.010
## 842 RI =~ C_CR4 0.045 0.022 0.014 0.007 0.007
## 843 DECO =~ Im21 0.044 -0.008 -0.011 -0.008 -0.008
## 844 RI =~ Im17 0.043 0.012 0.007 0.006 0.006
## 845 Im1 ~~ Im7 0.042 -0.004 -0.004 -0.042 -0.042
## 846 Im3 ~~ C_CR3 0.041 -0.007 -0.007 -0.013 -0.013
## 847 Im16 ~~ Im6 0.041 -0.006 -0.006 -0.011 -0.011
## 848 Im13 ~~ C_CR4 0.039 0.009 0.009 0.012 0.012
## 849 Im14 ~~ C_REP2 0.039 -0.001 -0.001 -0.021 -0.021
## 850 Im16 ~~ Im17 0.038 -0.005 -0.005 -0.021 -0.021
## 851 Im11 ~~ C_CR3 0.037 0.011 0.011 0.010 0.010
## 852 BRAND =~ C_CR3 0.036 -0.010 -0.012 -0.006 -0.006
## 853 AFCOM =~ Im17 0.034 0.006 0.006 0.005 0.005
## 854 Im5 ~~ Im12 0.033 0.005 0.005 0.011 0.011
## 855 Im21 ~~ Im19 0.033 -0.006 -0.006 -0.011 -0.011
## 856 FOOD =~ COM_A4 0.033 -0.011 -0.009 -0.005 -0.005
## 857 Im11 ~~ SAT_3 0.031 -0.007 -0.007 -0.009 -0.009
## 858 Im3 ~~ Im6 0.031 0.003 0.003 0.010 0.010
## 859 BRAND ~~ AFCOM 0.031 -0.007 -0.006 -0.006 -0.006
## 860 ATMOS =~ SAT_3 0.031 -0.007 -0.008 -0.007 -0.007
## 861 C_CR1 ~~ C_CR4 0.030 -0.040 -0.040 -0.033 -0.033
## 862 PRODQUAL =~ C_REP1 0.029 0.006 0.004 0.006 0.006
## 863 DECO =~ Im14 0.026 0.003 0.004 0.005 0.005
## 864 DECO =~ Im10 0.026 -0.003 -0.004 -0.005 -0.005
## 865 RI =~ C_CR3 0.025 0.017 0.010 0.005 0.005
## 866 SAT =~ Im7 0.025 -0.007 -0.006 -0.005 -0.005
## 867 Im2 ~~ COM_A2 0.025 -0.004 -0.004 -0.009 -0.009
## 868 FOOD =~ Im22 0.023 0.009 0.007 0.005 0.005
## 869 DECO =~ C_CR3 0.020 0.007 0.009 0.004 0.004
## 870 Im6 ~~ C_CR3 0.020 -0.006 -0.006 -0.008 -0.008
## 871 Im7 ~~ SAT_1 0.019 0.003 0.003 0.016 0.016
## 872 BRAND =~ Im21 0.018 -0.006 -0.007 -0.005 -0.005
## 873 Im21 ~~ SAT_1 0.018 0.004 0.004 0.008 0.008
## 874 Im1 ~~ C_CR4 0.018 -0.005 -0.005 -0.015 -0.015
## 875 Im18 ~~ COM_A3 0.018 0.005 0.005 0.007 0.007
## 876 COI =~ SAT_1 0.017 0.003 0.004 0.004 0.004
## 877 COI =~ Im10 0.017 0.001 0.003 0.003 0.003
## 878 AFCOM =~ Im3 0.016 0.003 0.003 0.003 0.003
## 879 Im13 ~~ C_CR1 0.016 -0.005 -0.005 -0.008 -0.008
## 880 RI =~ SAT_3 0.016 -0.010 -0.006 -0.005 -0.005
## 881 Im20 ~~ C_CR4 0.016 0.007 0.007 0.007 0.007
## 882 PROF =~ Im10 0.016 0.004 0.004 0.005 0.005
## 883 PROF =~ Im14 0.016 -0.004 -0.004 -0.005 -0.005
## 884 Im2 ~~ SAT_3 0.016 -0.003 -0.003 -0.006 -0.006
## 885 COI =~ Im22 0.014 -0.003 -0.006 -0.004 -0.004
## 886 DECO =~ COM_A1 0.014 -0.004 -0.005 -0.004 -0.004
## 887 COM_A4 ~~ C_CR1 0.014 -0.007 -0.007 -0.007 -0.007
## 888 BRAND ~~ RI 0.013 -0.002 -0.004 -0.004 -0.004
## 889 Im6 ~~ COM_A4 0.013 -0.004 -0.004 -0.006 -0.006
## 890 Im21 ~~ Im6 0.013 -0.003 -0.003 -0.006 -0.006
## 891 COI =~ Im19 0.012 0.002 0.004 0.004 0.004
## 892 SAT_1 ~~ SAT_2 0.012 0.006 0.006 0.020 0.020
## 893 C_REP1 ~~ C_CR1 0.012 -0.003 -0.003 -0.007 -0.007
## 894 Im2 ~~ C_CR3 0.012 0.004 0.004 0.006 0.006
## 895 Im3 ~~ Im21 0.012 -0.002 -0.002 -0.006 -0.006
## 896 SAT_2 ~~ C_REP2 0.011 0.001 0.001 0.009 0.009
## 897 Im19 ~~ C_CR4 0.011 -0.005 -0.005 -0.007 -0.007
## 898 Im14 ~~ Im19 0.011 0.001 0.001 0.009 0.009
## 899 Im20 ~~ Im16 0.010 0.004 0.004 0.006 0.006
## 900 Im16 ~~ C_REP2 0.010 0.001 0.001 0.008 0.008
## 901 Im22 ~~ C_CR4 0.009 -0.005 -0.005 -0.006 -0.006
## 902 CHOICE ~~ COI 0.009 0.007 0.004 0.004 0.004
## 903 COI =~ Im17 0.009 0.002 0.003 0.002 0.002
## 904 COI =~ COM_A2 0.008 0.003 0.005 0.003 0.003
## 905 Im4 ~~ SAT_3 0.008 0.002 0.002 0.007 0.007
## 906 Im5 ~~ Im13 0.008 -0.003 -0.003 -0.005 -0.005
## 907 Im5 ~~ C_CR1 0.008 0.004 0.004 0.005 0.005
## 908 Im5 ~~ C_REP3 0.007 -0.001 -0.001 -0.004 -0.004
## 909 CHOICE =~ COM_A2 0.007 -0.003 -0.004 -0.002 -0.002
## 910 FRENCH =~ Im12 0.007 -0.003 -0.003 -0.003 -0.003
## 911 PRODQUAL =~ Im3 0.007 0.004 0.003 0.002 0.002
## 912 FRENCH =~ Im19 0.007 0.004 0.004 0.004 0.004
## 913 Im19 ~~ C_CR1 0.006 -0.003 -0.003 -0.005 -0.005
## 914 Im12 ~~ Im19 0.005 -0.002 -0.002 -0.005 -0.005
## 915 COI =~ Im20 0.005 -0.002 -0.003 -0.002 -0.002
## 916 FOOD =~ Im12 0.005 -0.004 -0.003 -0.003 -0.003
## 917 FOOD =~ Im17 0.004 0.003 0.003 0.002 0.002
## 918 FOOD =~ Im18 0.004 -0.003 -0.003 -0.002 -0.002
## 919 PRODQUAL =~ C_CR3 0.004 -0.006 -0.004 -0.002 -0.002
## 920 PROF ~ RI 0.003 0.004 0.003 0.003 0.003
## 921 Im4 ~~ Im13 0.003 -0.001 -0.001 -0.005 -0.005
## 922 PROF =~ COM_A4 0.003 -0.003 -0.003 -0.002 -0.002
## 923 Im11 ~~ C_REP3 0.003 0.001 0.001 0.003 0.003
## 924 Im1 ~~ Im19 0.003 -0.001 -0.001 -0.007 -0.007
## 925 CHOICE =~ Im7 0.003 0.002 0.002 0.002 0.002
## 926 Im1 ~~ C_REP1 0.003 -0.001 -0.001 -0.005 -0.005
## 927 Im16 ~~ COM_A2 0.002 0.002 0.002 0.003 0.003
## 928 Im18 ~~ SAT_3 0.002 0.002 0.002 0.002 0.002
## 929 CHOICE ~ Im9 0.002 -0.002 -0.001 -0.002 -0.001
## 930 COM_A3 ~~ C_CR4 0.002 0.003 0.003 0.003 0.003
## 931 FRENCH =~ Im4 0.002 0.001 0.001 0.001 0.001
## 932 RI =~ Im19 0.002 0.003 0.002 0.001 0.001
## 933 ATMOS ~ RI 0.001 0.007 0.003 0.003 0.003
## 934 Im21 ~~ C_REP2 0.001 0.000 0.000 0.003 0.003
## 935 Im10 ~~ Im22 0.001 -0.001 -0.001 -0.002 -0.002
## 936 Im12 ~~ Im1 0.001 0.000 0.000 -0.003 -0.003
## 937 PRODQUAL =~ SAT_3 0.000 -0.001 -0.001 -0.001 -0.001
## 938 PRODQUAL ~~ RI 0.000 0.000 -0.001 -0.001 -0.001
## 939 BRAND =~ COM_A1 0.000 -0.001 -0.001 -0.001 -0.001
## 940 Im3 ~~ Im16 0.000 0.000 0.000 0.001 0.001
## 941 DECO ~ RI 0.000 0.001 0.001 0.001 0.001
## 942 COI =~ Im18 0.000 0.000 0.000 0.000 0.000
## 943 PROF =~ C_REP2 0.000 0.000 0.000 0.000 0.000
## 944 ATMOS ~ COI 0.000 0.000 -0.001 -0.001 -0.001
## 945 DECO =~ Im16 0.000 0.000 0.000 0.000 0.000
## 946 DECO =~ Im19 0.000 0.000 0.000 0.000 0.000
## 947 CHOICE ~ RI 0.000 0.000 0.000 0.000 0.000